■Faculty | Faculty Division of Natural Sciences Research Group of Mathematics | |||

■Position | Professor |

Last Updated :2023/10/03

#### Name (Japanese)

Kobayashi#### Name (Kana)

Tsuyoshi

- Apr. 2013, 9999, Nara Women's University, 理学部, 教授, Japan
- 2006, 2012, 奈良女子大学大学院人間文化研究科教授
- 2012, 奈良女子大学研究院自然科学系
- 2012, Division of Natural Sciences
- 1997, 2006, 奈良女子大学理学部教授
- 1997, 2006, Professor, Faculty of Science, Nara Women's University
- 1993, 1997, 奈良女子大学理学部助教授
- 1993, 1997, Associate Professor, Faculty of Science, Nara Women's University
- 1990, 1993, 大阪大学理学部講師
- 1990, 1993, Assistant Professor, Faculty of Science, Osaka University
- 1986, 1989, 大阪大学理学部助手
- 1986, 1989, Research Associate, Faculty of Science, Osaka Univeristy

- 2019, 22, 1, 45, 63, http://dx.doi.org/10.17654/GT022010045
- 2019, 22, 2, 129, 163, http://dx.doi.org/10.17654/GT022020129
- Refereed, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, WORLD SCIENTIFIC PUBL CO PTE LTD, A distance on the equivalence classes of spherical curves generated by deformations of type RI, Funakoshi, Yukari; Hashizume, Megumi; Ito, Noboru; Kobayashi, Tsuyoshi; Murai, Hiroko, In this paper, we introduce a distance (d) over bar (w)(3) on the equivalence classes of spherical curves under deformations of type RI and ambient isotopies. We obtain an inequality that estimate its lower bound (Theorem 1). In Theorem 2, we show that if for a pair of spherical curves P and P', (d) over bar (w)(3)([P],[P']) = 1 and P and P' satisfy a certain technical condition, then P' is obtained from P by a single weak RIII only. In Theorem 3, we show that if P and P' satisfy other conditions, then P' is ambient isotopic to a spherical curve that is obtained from P by a sequence of a particular local deformations, which realizes (d) over bar (w)(3)([P], [P'])., Oct. 2018, 27, 12, Scientific journal, 10.1142/S0218216518500669
- Refereed, Pacific Journal of Mathematics, University of California, Berkeley, The growth rate of the tunnel number of m-small knots, Tsuyoshi Kobayashi; Yo'av Rieck, In a previous paper, we defined the growth rate of the tunnel number of knots, an invariant that measures the asymptotic behavior of the tunnel number under connected sum. In this paper we calculate the growth rate of the tunnel number of m-small knots in terms of their bridge indices., 2018, 295, 1, 57, 101, Scientific journal, 10.2140/pjm.2018.295.57
- Refereed, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, AMER MATHEMATICAL SOC, THE SPECTRUM OF THE GROWTH RATE OF THE TUNNEL NUMBER IS INFINITE, Kenneth L. Baker; Tsuyoshi Kobayashi; Yo'av Rieck, For any epsilon > 0 we construct a hyperbolic knot K subset of S-3 for which 1 - epsilon < gr(t)(K) < 1. This shows that the spectrum of the growth rate of the tunnel number is infinite., Aug. 2016, 144, 8, 3609, 3618, Scientific journal, 10.1090/proc/12957
- Refereed, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, OXFORD UNIV PRESS, A knot with destabilized bridge spheres of arbitrarily high bridge number, Yeonhee Jang; Tsuyoshi Kobayashi; Makoto Ozawa; Kazuto Takao, We show that there exists an infinite family of knots, each of which has, for each integer k >= 0, a destabilized (2k + 5)-bridge sphere. We also show that, for each integer n >= 4, there exists a knot with a destabilized 3-bridge sphere and a destabilized n-bridge sphere., Apr. 2016, 93, 379, 396, Scientific journal, 10.1112/jlms/jdw004
- Refereed, TOPOLOGY AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, Bridge splittings of links with distance exactly n, Ayako Ido; Yeonhee Jang; Tsuyoshi Kobayashi, We show that, for any integers n >= 2, g >= 0 and b >= 1 except for (g, b) = (0,1) and (0, 2), there exists a (g, b)-bridge splitting of a link in some manifold with distance exactly n. (C) 2015 Elsevier B.V. All rights reserved., Dec. 2015, 196, 608, 617, Scientific journal, 10.1016/j.topol.2015.05.028
- Refereed, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, AMER MATHEMATICAL SOC, STRONG CYLINDRICALITY AND THE MONODROMY OF BUNDLES, Kazuhiro Ichihara; Tsuyoshi Kobayashi; YO'Av Rieck, A surface F in a 3-manifold M is called cylindrical if M cut open along F admits an essential annulus A. If, in addition, (A, partial derivative A) is embedded in (M, F), then we say that F is strongly cylindrical. Let M be a connected 3-manifold that admits a triangulation using t tetrahedra and F a two-sided connected essential closed surface of genus g(F). We show that if g(F) is at least 38t, then F is strongly cylindrical. As a corollary, we give an alternative proof of the assertion that every closed hyperbolic 3-manifold admits only finitely many fibrations over the circle with connected fiber whose translation distance is not one, which was originally proved by Saul Schleimer., Jul. 2015, 143, 7, 3169, 3176, Scientific journal, 10.1090/S0002-9939-2015-12473-2
- Refereed, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, INT PRESS BOSTON, INC, Hyperbolic volume and Heegaard distance, Tsuyoshi Kobayashi; Yo'av Rieck, We prove (Theorem 1.5) that there exists a constant Lambda > 0 so that if M is a (mu, d)-generic complete hyperbolic 3-manifold of volume Vol(M) < infinity and Sigma subset of M is a Heegaard surface of genus g(Sigma) > Lambda Vol(M), then d(Sigma) <= 2, where d(Sigma) denotes the distance of E as defined by Hempel. The term (mu,d)-generic is described precisely in Definition 1.3; see also Remark 1.4. The key for the proof of Theorem 1.5 is Theorem 1.8 which is of independent interest. There we prove that if M is a compact 3-manifold that can be triangulated using at most t tetrahedra (possibly with missing or truncated vertices), and Sigma is a Heegaard surface for M with g(Sigma) >= 76t + 26, then d(Sigma) <= 2., Mar. 2014, 22, 2, 247, 268, Scientific journal, 10.4310/CAG.2014.v22.n2.a3
- Refereed, ALGEBRAIC AND GEOMETRIC TOPOLOGY, GEOMETRY & TOPOLOGY PUBLICATIONS, Heegaard splittings of distance exactly n, Ayako Ido; Yeonhee Jang; Tsuyoshi Kobayashi, In this paper, we show that, for any integers n >= 2 and g >= 2, there exist genus-g Heegaard splittings of compact 3-manifolds with distance exactly n., 2014, 14, 3, 1395, 1411, Scientific journal, 10.2140/agt.2014.14.1395
- Refereed, TOPOLOGY AND GEOMETRY IN DIMENSION THREE: TRIANGULATIONS, INVARIANTS, AND GEOMETRIC STRUCTURES, AMER MATHEMATICAL SOC, A linear bound on the tetrahedral number of manifolds of bounded volume (after Jorgensen and Thurston), Tsuyoshi Kobayashi; Yo'av Rieck, 2011, 560, 27, +, International conference proceedings
- Refereed, TOPOLOGY AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, Destabilizing Heegaard splittings of knot exteriors, Tsuyoshi Kobayashi; Toshio Saito, We give a necessary and sufficient condition for Heegaard splittings of knot exteriors to admit destabilizations. As an application. we show the following: let K-1 and K-2 be a pair of knots which is introduced by Morimoto as an example giving degeneration of tunnel number under connected sum. The Heegaard splitting of the exterior of K-1 # K-2 derived from certain minimal unknotting tunnel systems of K-1 and K-2 is stabilized. (c) 2009 Elsevier B.V. All rights reserved., Jan. 2010, 157, 1, 202, 212, Scientific journal, 10.1016/j.topol.2009.04.059
- Refereed, TOPOLOGY AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, A design for pseudo-Anosov braids using hypotrochoid curves, Tsuyoshi Kobayashi; Saki Umeda, We make use of hypotrochoid Curves to propose mixing devices with simple mechanism. which gives pseudo-Anosov mixings. We exhibit some experiments to see the efficiency of the device. (c) 2009 Elsevier B.V. All rights reserved,, Jan. 2010, 157, 1, 280, 289, Scientific journal, 10.1016/j.topol.2009.04.061
- Refereed, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, INT PRESS BOSTON, INC, Manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings, Tsuyoshi Kobayashi; Yo' av Rieck, We construct infinitely many manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings. Both closed manifolds and manifolds with boundary tori are constructed., Oct. 2009, 17, 4, 637, 649, Scientific journal
- Refereed, TOPOLOGY AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, Knots with g(E(K))=2 and g(E(K # K # K))=6 and Morimoto's Conjecture, Tsuyoshi Kobayashi; Yo'av Rieck, We show that there exist knots K subset of S-3 with g(E(K)) = 2 and g(E(K # K # K)) = 6. Together with [Tsuyoshi Kobayashi, Yo'av Rieck, On the growth rate of the tunnel number of knots, J. Reine Angew. Math. 592 (2006) 63-78, Theorem 1.5], this proves existence of counterexamples to Morimoto's Conjecture [Kanji Morimoto, On the super additivity of tunnel number of knots, Math. Ann. 317 (3) (2000) 489-508]. This is a special case of [Tsuyoshi Kobayashi, Yo'av Rieck, Knot exteriors with additive Heegaard genus and Morimoto's Conjecture, Algebr. Geom. Topol. 8 (2008) 953-969, preprint version available at http://arxiv.org/abs/math.GT/0701765, 2007]. (C) 2008 Published by Elsevier B.V., Mar. 2009, 156, 6, 1114, 1117, Scientific journal, 10.1016/j.topol.2008.10.003
- Refereed, MATHEMATISCHE ANNALEN, SPRINGER, The amalgamation of high distance Heegaard splittings is always efficient, Tsuyoshi Kobayashi; Ruifeng Qiu, Let M be a compact orientable manifold, and F be an essential closed surface which cuts M into two 3-manifolds M (1) and M (2). Let M-i = V-i boolean OR(Si) W-i be a Heegaard splitting for i = 1, 2. We denote by d(S-i) the distance of V-i boolean OR(Si) W-i. If d(S-1), d(S-2) >= 2(g(M-1) + g(M-2) - g(F)), then M has a unique minimal Heegaard splitting up to isotopy, i. e. the amalgamation of V1 boolean OR(S1) W-1 and V-2 boolean OR(S2) W-2., Jul. 2008, 341, 3, 707, 715, Scientific journal, 10.1007/s00208-008-0214-7
- Not Refereed, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, OXFORD UNIV PRESS, Seifert surfaces in open books, and a new coding algorithm for links, Rei Furihata; Mikami Hirasawa; Tsuyoshi Kobayashi, We show that for any link L, there exists a Seifert surface for L that is obtained by successively plumbing flat annuli to a disk D, where the gluing regions are all in D. This furnishes a new way of coding links. We also present an algorithm to read the code directly from a braid presentation., Jun. 2008, 40, 3, 405, 414, Scientific journal, 10.1112/blms/bdn020
- Refereed, ALGEBRAIC AND GEOMETRIC TOPOLOGY, GEOMETRY & TOPOLOGY PUBLICATIONS, Knot exteriors with additive Heegaard genus and Morimoto's Conjecture, Tsuyoshi Kobayashi; Yo' av Rieck, Given integers g >= 2, n >= 1 we prove that there exist a collection of knots, denoted by K(g,n), fulfilling the following two conditions: (1) For any integer 2 <= h <= g, there exist infinitely many knots K is an element of K(g,n) with g(E(K)) = h. (2) For any m <= n, and for any collection of knots K(1),..., K(m) is an element of K(g,n), the Heegaard genus is additive: g(E(#(m)(i=1) K(i))) = Sigma(m)(i=1) g(E(K(i))). This implies the existence of counterexamples to Morimoto's Conjecture [17]., 2008, 8, 2, 953, 969, Scientific journal, 10.2140/agt.2008.8.953
- Refereed, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, INT PRESS CO LTD, Heegaard genus of the connected sum of m-small knots, Tsuyoshi Kobayashi; Yo'av Rieck, We prove that if K-1 subset of M-1,..., K-n subset of M-n are m-small knots in closed orientable 3-manifolds, then the Heegaard genus of E(#K-n(i=1)i) is strictly less than the sum of the Heegaard genera of the E (K-i) (i = 1,..., n) if and only if there exists a proper subset I of {1,...,n} so that #K-i is an element of I(i) admits a primitive meridian. This generalizes the main result of Morimoto [On the super additivity of tunnel number of knots, Math. Ann. 317 (2000), 489-508]., Dec. 2006, 14, 5, 1037, 1077, Scientific journal
- Refereed, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, WALTER DE GRUYTER & CO, On the growth rate of the tunnel number of knots, Tsuyoshi Kobayashi; Yo'av Rieck, Given a knot K in a closed orientable manifold M we define the growth rate of the tunnel number of K to be gr(t) (K) = lim sup(n ->infinity) t(nK) - nt(K)/n - 1.As our main result n we prove that the Heegaard genus of M is strictly less than the Heegaard genus of the knot exterior if and only if the growth rate is less than 1. In particular this shows that a non-trivial knot in S-3 is never asymptotically super additive. The main result gives conditions that imply falsehood of Morimoto's Conjecture., 2006, 592, 63, 78, Scientific journal, 10.1515/CRELLE.2006.023
- Refereed, Japanese Journal of Mathematics, Essential laminations and branched surfaces in the exteriors of links, Mark Brittenham; Chuichiro Hayashi; Mikami Hirasawa; Tsuyoshi Kobayashi; Koya Shimokawa, 2005, 31, 1, 25, 96, Scientific journal, 10.4099/math1924.31.25
- Refereed, ALGEBRAIC AND GEOMETRIC TOPOLOGY, GEOMETRY & TOPOLOGY PUBLICATIONS, A search method for thin positions of links, Daniel J. Heath; Tsuyoshi Kobayashi, We give a method for searching for thin positions of a given link., 2005, 5, 1027, 1050, Scientific journal
- Refereed, MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, CAMBRIDGE UNIV PRESS, Separating incompressible surfaces and stabilizations of Heegaard splittings, T Kobayashi; RF Qiu; YA Rieck; SC Wang, We describe probably the simplest 3-manifold which contains closed separating incompressible surfaces of arbitrarily large genus. Two applications of this observation are given. (1) For any closed, orientable 3-manifold M and any integer m > 0, a, surgery on a link in M of at most 2m + 1 components will provide a closed, orientable, irreducible 3-manifold containing m disjoint, non-parallel, separating, incompressible surfaces of arbitrarily high genus. (2) There exists a 3-manifold M containing separating imcompressible surfaces S-n of genus g(S-n) arbitrarily large, such that the amalgamation of minimal Heegaard splittings of two resulting 3-manifolds cutting along S-n can be stabilized g(S-n) - 3 times to a minimal Heegaard splitting of M., Nov. 2004, 137, 633, 643, Scientific journal, 10.1017/S0305004104007790
- Refereed, TOPOLOGY AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, Local detection of strongly irreducible Heegaard splittings via knot exteriors, T Kobayashi; Y Rieck, Let H-1 boolean ORSigma H-2 be a strongly irreducible Heegaard splitting of a 3-manifold M other than S-3, and X a 3-dimensional submanifold of M such that: (1) X is homeomorphic to the exterior of a non-trivial knot in S-3, and (2) there is a compressing disk, say D-X, of partial derivative X such that partial derivative D-X is a meridian curve of X. Suppose that partial derivative X boolean AND Sigma consists of a non-empty collection of simple closed curves which are essential in both partial derivative X and Sigma. Then we show that: (1) the closure of some component of Sigma\ partial derivative X is an annulus and is parallel to an annulus in partial derivative X, and (2) each component of Sigma boolean AND X is a (possibly boundary parallel) meridional annulus. (C) 2003 Elsevier B.V. All rights reserved., Mar. 2004, 138, 1-3, 239, 251, Scientific journal, 10.1016/j.topol.2003.08.005
- Refereed, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, WORLD SCIENTIFIC PUBL CO PTE LTD, Scharlemann-Thompson untelescoping of Heegaard splittings is finer than Casson-Gordon's, T Kobayashi, We show that there exist infinitely many 3-manifolds M, each of which admits a genus 4 Heegaard splitting V boolean ORP W such that there is a Scharlemann-Thompson untelescoping of V boolean ORP W which decomposes M into three pieces, and that any Casson-Gordon untelescoping of V boolean ORP W decomposes M into exactly two pieces., Nov. 2003, 12, 7, 877, 891, Scientific journal, 10.1142/S0218216503002810
- Refereed, Kobe J. Math., Kobe University, Locally Thin Position for a Link(共著), KOBAYASHI Tsuyoshi, 2003, 20, 1, 1, 10
- Refereed, GEOMETRY & TOPOLOGY, GEOMETRY & TOPOLOGY PUBLICATIONS, Heegaard splittings of exteriors of two bridge knots, Tsuyoshi Kobayashi, In this paper, we show that, for each non-trivial two bridge knot K and for each g >= 3, every genus g Heegaard splitting of the exterior E(K) of K is reducible., 2001, 5, 609, 650, Scientific journal
- Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, Pre-taut sutured manifolds and essential laminations, M Hirasawa; T Kobayashi, Dec. 2001, 38, 4, 905, 922, Scientific journal
- Refereed, PACIFIC JOURNAL OF MATHEMATICS, PACIFIC JOURNAL MATHEMATICS, The Rubinstein-Scharlemann graphic of a 3-manifold as the discriminant set of a stable map, T Kobayashi; O Saeki, We show that Rubinstein-Scharlemann graphics for 3-manifolds can be regarded as the images of the singular sets (: discriminant set) of stable maps from the 3-manifolds into the plane. As applications of our understanding of the graphic, we give a method for describing Heegaard surfaces in 3-manifolds by using arcs in the plane, and give an orbifold version of Rubinstein-Scharlemann's setting. Then by using this setting, we show that every genus one 1-bridge position of a nontrivial two bridge knot is obtained from a 2-bridge position in a standard manner., Sep. 2000, 195, 1, 101, 156, Scientific journal
- Refereed, Geometry and Topology Monographs, Classification of unknotting tunnels for two bridge knots, KOBAYASHI Tsuyoshi, 1999, 2, 259, 290
- Refereed, PACIFIC JOURNAL OF MATHEMATICS, PACIFIC JOURNAL MATHEMATICS, Essential tangle decomposition from thin position of a link, DJ Heath; T Kobayashi, In this paper, we develop the idea of Thompson which treats the relationship between bridge position, incompressible meridianal planar surfaces, and thin position. We show that for a link in thin position there exits a canonical depth 1 nested tangle decomposition with incompressible a-spheres arising from the thin position (Proposition 3.7), and we show that there is a maximal essential tangle decomposition of the link that is closely related to the thin position (Theorem 4.3)., May 1997, 179, 1, 101, 117, Scientific journal
- Refereed, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, WORLD SCIENTIFIC PUBL CO PTE LTD, On canonical genus and free genus of knot, M Kobayashi; T Kobayashi, We show that the differences between canonical genus and free genus, and differences between free genus and usual genus of a knot can be arbitrarily large., Feb. 1996, 5, 1, 77, 85, Scientific journal
- Refereed, Kobe Journal of Mathematics, Kobe University, Example of hyperbolic knot which do not admit depth 1 foliation, KOBAYASHI Tsuyoshi, 1996, 13, 2, 209, 221
- Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, A NECESSARY AND SUFFICIENT CONDITION FOR A 3-MANIFOLD TO HAVE GENUS-G HEEGAARD SPLITTING (A PROOF OF HASS-THOMPSON CONJECTURE), T KOBAYASHI; H NISHI, Mar. 1994, 31, 1, 109, 136, Scientific journal
- Refereed, Journal of knot theory and its ramification, A construction of arbitrarily high degeneration of tunnel numbers of knots under connected sum, KOBAYASHI Tsuyoshi, 1994, 3, 179, 186
- Refereed, Proc. Applied Math. Workshop KAIST, Knots which are prime on band connected sum, KOBAYASHI Tsuyoshi, 1994, 4, 79, 89
- Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, A CONSTRUCTION OF 3-MANIFOLDS WHOSE HOMEOMORPHISM CLASSES OF HEEGAARD-SPLITTINGS HAVE POLYNOMIAL-GROWTH, T KOBAYASHI, Dec. 1992, 29, 4, 653, 674, Scientific journal
- Refereed, Knots 90, Fibered links which are band connected sum of two links, KOBAYASHI Tsuyoshi, 1992, 9, 23
- Refereed, MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, CAMBRIDGE UNIV PRESS, A CRITERION FOR DETECTING INEQUIVALENT TUNNELS FOR A KNOT, T KOBAYASHI, May 1990, 107, 483, 491, Scientific journal
- Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, FIBERED LINKS AND UNKNOTTING OPERATIONS, T KOBAYASHI, Dec. 1989, 26, 4, 699, 742, Scientific journal
- Refereed, TOPOLOGY AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, UNIQUENESS OF MINIMAL GENUS SEIFERT SURFACES FOR LINKS, T KOBAYASHI, Nov. 1989, 33, 3, 265, 279, Scientific journal
- Refereed, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, AMER MATHEMATICAL SOC, GENERALIZED UNKNOTTING OPERATIONS AND TANGLE DECOMPOSITIONS, T KOBAYASHI, Feb. 1989, 105, 2, 471, 478, Scientific journal
- Refereed, Kobe J. Math., Kobe University, Minimal genus Seifert surfaces for unknotting number 1 knots, KOBAYASHI Tsuyoshi, 1989, 6, 1, 53, 62
- Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, CASSON-GORDON RECTANGLE CONDITION OF HEEGAARD DIAGRAMS AND INCOMPRESSIBLE TORI IN 3-MANIFOLDS, T KOBAYASHI, Sep. 1988, 25, 3, 553, 573, Scientific journal
- Refereed, Contemporary math., Heights of simple loops and pseudo-Anosov homeomorphisms, KOBAYASHI Tsuyoshi, 1988, 78, 327, 338
- Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, CYCLOTOMIC INVARIANTS FOR LINKS, T KOBAYASHI; H MURAKAMI; J MURAKAMI, Sep. 1988, 64, 7, 235, 238, Scientific journal
- Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, PSEUDO-ANOSOV HOMEOMORPHISMS WHICH EXTEND TO ORIENTATION REVERSING HOMEOMORPHISMS OF S3, T KOBAYASHI, Dec. 1987, 24, 4, 739, 743, Scientific journal
- Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, STRUCTURES OF FULL HAKEN MANIFOLDS, T KOBAYASHI, Mar. 1987, 24, 1, 173, 215, Scientific journal
- Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, HOMEOMORPHISMS OF 3-MANIFOLDS AND TOPOLOGICAL-ENTROPY, T KOBAYASHI, 1985, 22, 2, 289, 297, Scientific journal
- Refereed, INVENTIONES MATHEMATICAE, SPRINGER VERLAG, LINKS OF HOMEOMORPHISMS OF A DISK AND TOPOLOGICAL-ENTROPY, T KOBAYASHI, 1985, 80, 1, 153, 159, Scientific journal
- Refereed, TOPOLOGY AND ITS APPLICATIONS, ELSEVIER SCIENCE BV, PRIMITIVE LINKS OF NON-SINGULAR MORSE-SMALE FLOWS ON THE SPECIAL SEIFERT FIBERED MANIFOLDS, T KOBAYASHI, 1985, 20, 1, 67, 78, Scientific journal
- Refereed, Japan J. Math., The Mathematical Society of Japan, On 3-manifolds with no periodic maps(共著), KOBAYASHI Tsuyoshi, 1984, 10, 2, 185--193, 193, 10.4099/math1924.10.185
- Refereed, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, MATH SOC JAPAN, NON-SEPARATING INCOMPRESSIBLE TORI IN 3-MANIFOLDS, T KOBAYASHI, 1984, 36, 1, 11, 22, Scientific journal
- Refereed, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, AMER MATHEMATICAL SOC, 3-MANIFOLDS WHICH CONTAIN NONPARALLEL PROJECTIVE-PLANES, T KOBAYASHI, 1984, 91, 2, 314, 318, Scientific journal
- Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, LINKS OF HOMEOMORPHISMS OF SURFACES AND TOPOLOGICAL-ENTROPY, T KOBAYASHI, 1984, 60, 10, 381, 383, Scientific journal
- Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, STRUCTURES OF THE HAKEN MANIFOLDS WITH HEEGAARD-SPLITTINGS OF GENUS-2, T KOBAYASHI, 1984, 21, 2, 437, 455, Scientific journal
- Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, EQUIVARIANT ANNULUS THEOREM FOR 3-MANIFOLDS, T KOBAYASHI, 1983, 59, 8, 403, 406, Scientific journal
- Refereed, Adv. Stud. Pure Math., MATH SOC JAPAN, On keen Heegaard splittings, Ayako Ido; Yeonhee Jang; Tsuyoshi Kobayashi, In this paper, we introduce a new concept of strongly keen for Heegaard splittings, and show that, for any integers n > 2 and g > 3, there exists a strongly keen Heegaard splitting of genus g whose Hempel distance is n., Oct. 2018, 78, 293, 311, International conference proceedings
- Refereed, JP Journal of Geometry and Topology, Stable Double Point Numbers of Pairs of Spherical Curves, Tsuyoshi Kobayashi, Sumika Kobayashi, May 2019, 22, 2, 129, 163, Scientific journal

- Not Refereed, RIMS kokyuroku, Extending geodesics in the curve complex, Jang Yeonhee; Ayako Ido; Tsuyoshi Kobayashi, 2013, 1836, 1, 6
- 数理解析研究所講究録, 京都大学数理解析研究所, (1,1)-BRIDGE SPLITTINGS WITH DISTANCE EXECTLY $n$ (Pursuit of the Essence of Singularity Theory), IDO AYAKO; JANG YEONHEE; KOBAYASHI TSUYOSHI, Dec. 2013, 1868, 32, 37
- RIMS Kokyuroku, Kyoto University, LINKS OF EMBEDDINGS OF SURFACES AND TOPOLOGICAL ENTROPY(Theory of Dynamical Systems and Its Application to Nonlinear Problems), KOBAYASHI Tsuyoshi, Sep. 1984, 536, 37, 44
- RIMS Kokyuroku, Kyoto University, Minimal genus Seifert surfaces for unknotting number 1 knots, Kobayashi Tsuyoshi, Dec. 1987, 636, 1, 15
- RIMS Kokyuroku, Kyoto University, Heights of simple loops and pseudo-Anosov homeomorphisms, Kobayashi Tsuyoshi, May 1987, 624, 170, 193
- RIMS Kokyuroku, Kyoto University, Detecting atoroidal 3-manifolds, KOBAYASHI Tsuyoshi, Feb. 1987, 605, 45, 62
- RIMS Kokyuroku, Kyoto University, Structures of the Haken manifolds with heegaard splittings of genus two, Kobayashi Tsuyoshi, May 1983, 487, 1, 17

- Realizing pseudo-Anosov egg beaters with simple mechanisms, In:Proceedings of the International Workshop on Knot Theory for Scientific Objects held in Osaka(Japan), March 8-10, Osaka Municipal Universities Press, 2007, Not Refereed
- Realizing pseudo-Anosov egg beaters with simple mechanisms, In:Proceedings of the International Workshop on Knot Theory for Scientific Objects held in Osaka(Japan), March 8-10, Osaka Municipal Universities Press, 2007, Not Refereed
- Links of embeddings of surfaces and topological entropy, In: The theory of dynamical systems and its applications to nonlinear problems (1984), World Sci. Publ. Co. Ltd., 1984, Not Refereed
- Links of embeddings of surfaces and topological entropy, In: The theory of dynamical systems and its applications to nonlinear problems (1984), World Sci. Publ. Co. Ltd., 1984, Not Refereed

- Oral presentation, 23 Dec. 2021, 26 Dec. 2021
- Invited oral presentation, 09 Nov. 2020, 11 Nov. 2020
- トポロジーとコンピュータ, 折り紙に現れる幾つかの数学構造について, Invited oral presentation, 2017
- 結び目の数学X, Complexes induced from spherical curves and distances, 2017
- Knotting Nagoya, 折り紙の数学入門, 2016
- Low dimensional topology and number theory VII, A construction of flat-foldable origami via similarity structure, 2015
- Low dimensional topology and number theory VII, A construction of flat-foldable origami via similarity structure, 2015
- Topology and Geometry of Low-dimensional Manifolds, On keen Heegaard splitting, 2014
- Topology and Geometry of Low-dimensional Manifolds, On keen Heegaard splitting, 2014
- Spring Workshop 2013 on Low-Dimensional Topology and its Ramifications, 2次元トーラスの相似構造を用いた一般化されたミウラ折りの構成, 2013
- 位相数学・微分幾何学国際会議 兼第6回日本―メキシコ位相数学合同シンポジウム（同時開催）, Heegaard splittings of distance $n$(joint work with Ayako Ido and Yeonhee Jang), 2013
- Spring Workshop 2013 on Low-Dimensional Topology and its Ramifications, A construction of generaliza Mirura folding via similarity structure on 2-dimensional torus, 2013
- International Conference on Topology and Geometry 2013 Joint with the 6th Japan-Mexico Topology Symposium, Heegaard splittings of distance $n$(joint work with Ayako Ido and Yeonhee Jang), 2013
- 日大トポロジーセミナー, Heegaard splitting with distance exactly n for each non-negative integer n, 2012
- Workshop on Low Dimensional Topology in Shanghai and Suzhou, On the growth rate of tunnel numbers of knots, 2011
- Workshop on Low Dimensional Topology in Shanghai and Suzhou, On the growth rate of tunnel numbers of knots, 2011
- E-KOOKセミナー2010, Toward Haken type theorems for essential laminations in 3-manifolds: Proposal of fundamental settings and applications, 2010
- Simplicial Complexes Arising in Low-Dimensional Topology, Realization problems of distances of Heegaard splittings, 2009
- Category Theory, Computer Science, and Topology, On thin presentations of 3-manifolds and links, 2009
- Tsuyoshi Kobayashi, Mathematical Science of Knots, On keen bridge splittings of links, 25 Dec. 2021, 23 Dec. 2021, 26 Dec. 2021

- 2013, 2016, 25400091, Principal investigator
- 2017, 2020, 17K05249, Principal investigator
- 2017, 2020, 17K05249, Principal investigator
- 2017, 2020, 17K05249, Principal investigator
- 2022, 2025, 22K03313, Principal investigator
- 応用トポロジー, 0, 0, 0, Competitive research funding
- 低次元トポロジー, 0, 0, 0, Competitive research funding, rm:presentations
- Low dimensional topology, 0, 0, 0, Competitive research funding, rm:presentations