研究者総覧

小林 毅KOBAYASHI Tsuyoshiコバヤシ ツヨシ

所属部署名研究院自然科学系数学領域
職名教授
Last Updated :2022/10/06

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プロフィール情報

  • 小林, コバヤシ
  • 毅, ツヨシ

学位

  • 理学博士, 大阪大学
  • 理学修士, 大阪大学

研究キーワード

  • 位相的データ解析
  • 三次元多様体論
  • 結び目理論
  • 位相幾何学
  • Topological data analysis
  • 3-manifild
  • knot
  • Topology

研究分野

  • 自然科学一般, 幾何学

経歴

  • 2013年04月, 9999年, 奈良獅子大学, 理学部, 教授, 日本国
  • 2006年, 2012年, :奈良女子大学大学院人間文化研究科教授
  • 2012年, -:奈良女子大学研究院自然科学系
  • 2012年, -:Division of Natural Sciences
  • 1997年, 2006年, :奈良女子大学理学部教授
  • 1997年, 2006年, :Professor, Faculty of Science, Nara Women's University
  • 1993年, 1997年, :奈良女子大学理学部助教授
  • 1993年, 1997年, :Associate Professor, Faculty of Science, Nara Women's University
  • 1990年, 1993年, :大阪大学理学部講師
  • 1990年, 1993年, :Assistant Professor, Faculty of Science, Osaka University
  • 1986年, 1989年, :大阪大学理学部助手
  • 1986年, 1989年, :Research Associate, Faculty of Science, Osaka Univeristy

学歴

  • 1986年, 大阪大学, 理学研究科, 数学, 日本国
  • 1981年, 大阪大学, 理学部, 数学, 日本国

所属学協会

  • アメリカ数学会
  • American Mathematical Society

Ⅱ.研究活動実績

論文

  • 英語, JP Jour. of Geometry and Topology, Pushpa Publishing House, SIMILARITY STRUCTURE ON 2-DIMENSIONAL TORUS AND FLAT ORIGAMI, 2019年, 22, 1, 45, 63
  • 英語, JP Jour. of Geometry and Topology, Pushpa Publishing House, STABLE DOUBLE POINT NUMBERS OF PAIRS OF SPHERICAL CURVES, 2019年, 22, 2, 129, 163
  • 査読あり, 英語, J. Knot Theory Ramifications, A distance on the equivalence classes of spherical curves generated by deformations of type RI, Yukari Funakoshi; Megumi Hashizume; Noboru Ito; Tsuyoshi Kobayashi; Hiroko Murai, 球面曲線全体における初の複体の導入.孤立特異点のうち,カスプと向きのそろった3重点を選び,その局所的な特異点のジャンプによるホモトピー同値類を考え3重点ジャンプの最小回数によって距離を導入, 距離1をedgeに対応させ複体を定義した.この論文以降,距離1の数学的結果がpath-complexをたどることで曲線全体の結果となる,というアプローチが初めて確立された.path complexのpathの長さと上記の距離の一致性を示し評価式を与え具体的な部分複体の決定をした., 2018年10月, 27, 12, 研究論文(学術雑誌)
  • 査読あり, 英語, Pacific Journal of Mathematics, 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年, 295, 1, 57, 101, 研究論文(学術雑誌)
  • 査読あり, 英語, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 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., 2016年08月, 144, 8, 3609, 3618, 研究論文(学術雑誌)
  • 査読あり, 英語, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 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., 2016年04月, 93, 379, 396, 研究論文(学術雑誌)
  • 査読あり, 英語, TOPOLOGY AND ITS APPLICATIONS, 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., 2015年12月, 196, 608, 617, 研究論文(学術雑誌)
  • 査読あり, 英語, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 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., 2015年07月, 143, 7, 3169, 3176, 研究論文(学術雑誌)
  • 査読あり, 英語, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 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., 2014年03月, 22, 2, 247, 268, 研究論文(学術雑誌)
  • 査読あり, 英語, ALGEBRAIC AND GEOMETRIC TOPOLOGY, 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年, 14, 3, 1395, 1411, 研究論文(学術雑誌)
  • 査読無し, その他, 京都大学数理解析研究所講究録, (1,1)-bridge splitting with distance exactly n,, 小林 毅; 井戸絢子; 張娟姫, 2013年, 1868, 32--37
  • 査読あり, 英語, TOPOLOGY AND GEOMETRY IN DIMENSION THREE: TRIANGULATIONS, INVARIANTS, AND GEOMETRIC STRUCTURES, A linear bound on the tetrahedral number of manifolds of bounded volume (after Jorgensen and Thurston), Tsuyoshi Kobayashi; Yo'av Rieck, 2011年, 560, 27, +, 研究論文(国際会議プロシーディングス)
  • 査読あり, 英語, TOPOLOGY AND ITS APPLICATIONS, 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., 2010年01月, 157, 1, 202, 212, 研究論文(学術雑誌)
  • 査読あり, 英語, TOPOLOGY AND ITS APPLICATIONS, 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,, 2010年01月, 157, 1, 280, 289, 研究論文(学術雑誌)
  • 査読あり, 英語, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 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., 2009年10月, 17, 4, 637, 649, 研究論文(学術雑誌)
  • 査読あり, 英語, TOPOLOGY AND ITS APPLICATIONS, 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., 2009年03月, 156, 6, 1114, 1117, 研究論文(学術雑誌)
  • 査読あり, 英語, MATHEMATISCHE ANNALEN, 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., 2008年07月, 341, 3, 707, 715, 研究論文(学術雑誌)
  • 査読無し, 英語, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 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., 2008年06月, 40, 3, 405, 414, 研究論文(学術雑誌)
  • 査読あり, 英語, ALGEBRAIC AND GEOMETRIC TOPOLOGY, 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年, 8, 2, 953, 969, 研究論文(学術雑誌)
  • 査読あり, 英語, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 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]., 2006年12月, 14, 5, 1037, 1077, 研究論文(学術雑誌)
  • 査読あり, 英語, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 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年, 592, 63, 78, 研究論文(学術雑誌)
  • 査読あり, 英語, Japanese Journal of Mathematics, Essential laminations and branched surfaces in the exterior of links(共著), 小林 毅, 2005年, 31, 1, 25, 96, 研究論文(学術雑誌)
  • 査読あり, 英語, Algebr. Geom. Topol., A search method for a thin position of a link(共著), 小林 毅; Daniel, Heath, We give a method for searching for thin positions of a given link., 2005年, 5, 1027, 1050, 研究論文(学術雑誌)
  • 査読あり, 英語, Math. Proc. Cambridge Phil. Soc., Separating incompressible surfaces and stabilizations of Heegaard splittings(共著), 小林 毅, 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., 2004年11月, 137, 633, 643, 研究論文(学術雑誌)
  • 査読あり, 英語, Topology and its Appl., Local detection of strongly irreducible Heegaard splittings via knot exteriors(共著), 小林 毅, 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., 2004年03月, 138, 1-3, 239, 251, 研究論文(学術雑誌)
  • 査読あり, 英語, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 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., 2003年11月, 12, 7, 877, 891, 研究論文(学術雑誌)
  • 査読あり, その他, Kobe J. Math., Locally Thin Position for a Link(共著), 小林 毅, 2003年, 20, 1, 10
  • 査読あり, 英語, GEOMETRY & TOPOLOGY, 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年, 5, 609, 650, 研究論文(学術雑誌)
  • 査読あり, 英語, Osaka J. Math., Pre-taut sutured manifolds and essential laminations(共著), 小林 毅, 2001年12月, 38, 4, 905, 922, 研究論文(学術雑誌)
  • 査読あり, 英語, Pacific Journal of Mathematics, Rubinstein-Scharlemann graphic of 3-manifold as the discriminant set of a stable map(共著), 小林 毅, 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., 2000年09月, 195, 1, 101, 156, 研究論文(学術雑誌)
  • 査読あり, その他, Geometry and Topology Monographs, Classification of unknotting tunnels for two bridge knots, 小林 毅, 1999年, 2, 259, 290
  • 査読あり, 英語, Pacific Journal of Mathematics, Essential tangle decomposition from thin position of a link(共著), 小林 毅, 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)., 1997年05月, 179, 1, 101, 117, 研究論文(学術雑誌)
  • 査読あり, 英語, Journal of knot theory and its ramification, On canonical genus and free genus of knot(共著), 小林 毅, 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., 1996年02月, 5, 1, 77, 85, 研究論文(学術雑誌)
  • 査読あり, 英語, Kobe Journal of Mathematics, 神戸大学, Example of hyperbolic knot which do not admit depth 1 foliation, 小林 毅, 1996年, 13, 2, 209, 221
  • 査読あり, 英語, Osaka Journal of Mathematics, A necessary and sufficient condition for a 3-manifold to have genus g Heagaard splitting (A proof of Hass-Thompson conjecture)(共著), 小林 毅, 1994年03月, 31, 1, 109, 136, 研究論文(学術雑誌)
  • 査読あり, その他, Journal of knot theory and its ramification, A construction of arbitrarily high degeneration of tunnel numbers of knots under connected sum, 小林 毅, 1994年, 3, 179, 186
  • 査読あり, その他, Proc. Applied Math. Workshop KAIST, Knots which are prime on band connected sum, 小林 毅, 1994年, 4, 79, 89
  • 査読あり, 英語, OSAKA JOURNAL OF MATHEMATICS, A CONSTRUCTION OF 3-MANIFOLDS WHOSE HOMEOMORPHISM CLASSES OF HEEGAARD-SPLITTINGS HAVE POLYNOMIAL-GROWTH, T KOBAYASHI, 1992年12月, 29, 4, 653, 674, 研究論文(学術雑誌)
  • 査読あり, その他, Knots 90, Fibered links which are band connected sum of two links, 小林 毅, 1992年, 9, 23
  • 査読あり, 英語, MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, A CRITERION FOR DETECTING INEQUIVALENT TUNNELS FOR A KNOT, T KOBAYASHI, 1990年05月, 107, 483, 491, 研究論文(学術雑誌)
  • 査読あり, 英語, OSAKA JOURNAL OF MATHEMATICS, FIBERED LINKS AND UNKNOTTING OPERATIONS, T KOBAYASHI, 1989年12月, 26, 4, 699, 742, 研究論文(学術雑誌)
  • 査読あり, 英語, TOPOLOGY AND ITS APPLICATIONS, UNIQUENESS OF MINIMAL GENUS SEIFERT SURFACES FOR LINKS, T KOBAYASHI, 1989年11月, 33, 3, 265, 279, 研究論文(学術雑誌)
  • 査読あり, 英語, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, GENERALIZED UNKNOTTING OPERATIONS AND TANGLE DECOMPOSITIONS, T KOBAYASHI, 1989年02月, 105, 2, 471, 478, 研究論文(学術雑誌)
  • 査読あり, その他, Kobe J. Math., Minimal genus Seifert surfaces for unknotting number 1 knots, 小林 毅, 1989年, 6, 53, 62
  • 査読あり, 英語, OSAKA JOURNAL OF MATHEMATICS, CASSON-GORDON RECTANGLE CONDITION OF HEEGAARD DIAGRAMS AND INCOMPRESSIBLE TORI IN 3-MANIFOLDS, T KOBAYASHI, 1988年09月, 25, 3, 553, 573, 研究論文(学術雑誌)
  • 査読あり, その他, Contemporary math., Heights of simple loops and pseudo-Anosov homeomorphisms, 小林 毅, 1988年, 78, 327, 338
  • 査読あり, 英語, Proc. Japan Acad., Cyclotomic invariants for links(共著), 小林 毅, 1988年09月, 64, 7, 235, 238, 研究論文(学術雑誌)
  • 査読あり, 英語, OSAKA JOURNAL OF MATHEMATICS, PSEUDO-ANOSOV HOMEOMORPHISMS WHICH EXTEND TO ORIENTATION REVERSING HOMEOMORPHISMS OF S3, T KOBAYASHI, 1987年12月, 24, 4, 739, 743, 研究論文(学術雑誌)
  • 査読あり, 英語, OSAKA JOURNAL OF MATHEMATICS, STRUCTURES OF FULL HAKEN MANIFOLDS, T KOBAYASHI, 1987年03月, 24, 1, 173, 215, 研究論文(学術雑誌)
  • 査読あり, 英語, OSAKA JOURNAL OF MATHEMATICS, HOMEOMORPHISMS OF 3-MANIFOLDS AND TOPOLOGICAL-ENTROPY, T KOBAYASHI, 1985年, 22, 2, 289, 297, 研究論文(学術雑誌)
  • 査読あり, 英語, INVENTIONES MATHEMATICAE, LINKS OF HOMEOMORPHISMS OF A DISK AND TOPOLOGICAL-ENTROPY, T KOBAYASHI, 1985年, 80, 1, 153, 159, 研究論文(学術雑誌)
  • 査読あり, 英語, TOPOLOGY AND ITS APPLICATIONS, PRIMITIVE LINKS OF NON-SINGULAR MORSE-SMALE FLOWS ON THE SPECIAL SEIFERT FIBERED MANIFOLDS, T KOBAYASHI, 1985年, 20, 1, 67, 78, 研究論文(学術雑誌)
  • 査読あり, 英語, Japan J. Math., 一般社団法人 日本数学会, On 3-manifolds with no periodic maps(共著), 小林 毅, 1984年, 10, 2, 185--193, 193
  • 査読あり, 英語, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, NON-SEPARATING INCOMPRESSIBLE TORI IN 3-MANIFOLDS, T KOBAYASHI, 1984年, 36, 1, 11, 22, 研究論文(学術雑誌)
  • 査読あり, 英語, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 3-MANIFOLDS WHICH CONTAIN NONPARALLEL PROJECTIVE-PLANES, T KOBAYASHI, 1984年, 91, 2, 314, 318, 研究論文(学術雑誌)
  • 査読あり, 英語, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, LINKS OF HOMEOMORPHISMS OF SURFACES AND TOPOLOGICAL-ENTROPY, T KOBAYASHI, 1984年, 60, 10, 381, 383, 研究論文(学術雑誌)
  • 査読あり, 英語, OSAKA JOURNAL OF MATHEMATICS, STRUCTURES OF THE HAKEN MANIFOLDS WITH HEEGAARD-SPLITTINGS OF GENUS-2, T KOBAYASHI, 1984年, 21, 2, 437, 455, 研究論文(学術雑誌)
  • 査読あり, 英語, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, EQUIVARIANT ANNULUS THEOREM FOR 3-MANIFOLDS, T KOBAYASHI, 1983年, 59, 8, 403, 406, 研究論文(学術雑誌)
  • 査読あり, 英語, Adv. Stud. Pure Math., 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., 2018年10月, 78, 293, 311, 研究論文(国際会議プロシーディングス)
  • 査読あり, 英語, JP Journal of Geometry and Topology, Stable Double Point Numbers of Pairs of Spherical Curves, 小林毅; 小林住香, 2019年05月, 22, 2, 129, 163, 研究論文(学術雑誌)
  • 査読あり, その他, JP Journal of Geometry and Topology, SIMILARITY STRUCTURE ON 2-DIMENSIONAL TORUS AND FLAT ORIGAMI, Miki Irii; Tsuyoshi Kobayashi; Hiroko Murai, 2019年01月31日, 22, 1, 45, 63, 研究論文(学術雑誌)

MISC

  • 査読無し, その他, RIMS kokyuroku, Extending geodesics in the curve complex, Jang Yeonhee; Ayako Ido; Tsuyoshi Kobayashi, 2013年, 1836, 1, 6
  • 英語, 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, 2013年12月, 1868, 32, 37
  • 英語, 数理解析研究所講究録, 京都大学, Graphic of 3-manifolds and its applications (Low-Dimensional Topology of Tomorrow), 小林 毅, 2002年06月, 1272, 68, 83
  • 英語, 数理解析研究所講究録, 京都大学, LINKS OF EMBEDDINGS OF SURFACES AND TOPOLOGICAL ENTROPY(Theory of Dynamical Systems and Its Application to Nonlinear Problems), 小林 毅, 1984年09月, 536, 37, 44
  • 英語, 数理解析研究所講究録, 京都大学, Minimal genus Seifert surfaces for unknotting number 1 knots, 小林 毅, 1987年12月, 636, 1, 15
  • 英語, 数理解析研究所講究録, 京都大学, Heights of simple loops and pseudo-Anosov homeomorphisms, 小林 毅, 1987年05月, 624, 170, 193
  • 英語, 数理解析研究所講究録, 京都大学, Detecting atoroidal 3-manifolds, 小林 毅, 1987年02月, 605, 45, 62
  • 日本語, 数理解析研究所講究録, 京都大学, Structures of the Haken manifolds with heegaard splittings of genus two, 小林 毅, 1983年05月, 487, 1, 17

書籍等出版物

  • 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年, その他, 査読無し, その他
  • 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年, その他, 査読無し, その他
  • 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年, その他, 査読無し, その他
  • 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年, その他, 査読無し, その他

講演・口頭発表等

  • Tsuyoshi Kobayashi, 国内, 結び目の数理IV, On keen bridge splittings of links, 口頭発表(一般), 2021年12月23日, 2021年12月26日, 日本語
  • 小林毅,村井紘子, 国際, Mathematics of quasiperiodic systems and related topics, A construction of flat-foldable origami via similarity structure of 2-dimensional torus, 口頭発表(招待・特別), 2020年11月09日, 2020年11月11日, 英語
  • 国内, 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, 口頭発表(招待・特別), 2017年, その他
  • 結び目の数学X, Complexes induced from spherical curves and distances, 2017年, その他
  • Knotting Nagoya, 折り紙の数学入門, 2016年, その他
  • Low dimensional topology and number theory VII, A construction of flat-foldable origami via similarity structure, 2015年, その他
  • Low dimensional topology and number theory VII, A construction of flat-foldable origami via similarity structure, 2015年, その他
  • Topology and Geometry of Low-dimensional Manifolds, On keen Heegaard splitting, 2014年, その他
  • Topology and Geometry of Low-dimensional Manifolds, On keen Heegaard splitting, 2014年, その他
  • 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年, その他
  • 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年, その他
  • Spring Workshop 2013 on Low-Dimensional Topology and its Ramifications, A construction of generaliza Mirura folding via similarity structure on 2-dimensional torus, 2013年, その他
  • 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年, その他
  • 日大トポロジーセミナー, Heegaard splitting with distance exactly n for each non-negative integer n, 2012年, その他
  • Workshop on Low Dimensional Topology in Shanghai and Suzhou, On the growth rate of tunnel numbers of knots, 2011年, その他
  • Workshop on Low Dimensional Topology in Shanghai and Suzhou, On the growth rate of tunnel numbers of knots, 2011年, その他
  • E-KOOKセミナー2010, Toward Haken type theorems for essential laminations in 3-manifolds: Proposal of fundamental settings and applications, 2010年, その他
  • Simplicial Complexes Arising in Low-Dimensional Topology, Realization problems of distances of Heegaard splittings, 2009年, その他
  • Category Theory, Computer Science, and Topology, On thin presentations of 3-manifolds and links, 2009年, その他
  • 小林毅, 結び目の数理IV, On keen bridge splittings of links, 2021年12月25日, 2021年12月23日, 2021年12月26日, 日本語, rm:research_project_id;rm:research_project_id

共同研究・競争的資金等の研究課題

  • 基盤研究(C), 2013年, 2016年, 25400091, 研究代表者, 三次元多様体の幾何学的手法による研究と展開
  • 基盤研究(C), 2017年, 2020年, 17K05249, 研究代表者, 低次元トポロジーの発展と展開
  • 基盤研究(C), 2017年, 2020年, 17K05249, 研究代表者
  • 基盤研究(C), 2017年, 2020年, 17K05249, 研究代表者, 低次元トポロジーの発展と展開
  • 基盤研究(C), 2017年, 2020年, 17K05249, 研究代表者, 低次元トポロジーの発展と展開
  • 応用トポロジー, 0, 0, 0, 競争的資金
  • 低次元トポロジー, 0, 0, 0, 競争的資金, rm:presentations
  • Low dimensional topology, 0, 0, 0, 競争的資金, rm:presentations

Ⅲ.社会連携活動実績

1.公的団体の委員等(審議会、国家試験委員、他大学評価委員,科研費審査委員等)

  • 奈良県立奈良高等学校, SSH運営指導委員会委員, 2021年年4月月1日, 2022年年3月月3日
  • 奈良県立清翔高等学校, SSH運営指導委員, 2020年年4月月1日, 2021年年3月月3日
  • 奈良県立奈良高等学校, SSH運営指導委員, 2020年年4月月1日, 2021年年3月月3日
  • 奈良県立清翔高等学校, SSH運営指導委員, 2019年年4月月1日, 2020年年3月月3日
  • 奈良県立奈良高等学校, SSH運営指導委員, 2019年年4月月1日, 2020年年3月月3日


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