## KOBAYASHI TsuyoshiFaculty Division of Natural Sciences Research Group of Mathematics Professor Attached Elementary School Principal, Attached Elementary School Contact： tsuyoshicc.nara-wu.ac.jp |

Last Updated :2021/10/20

- 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

- 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

- - 1986, Osaka University, 理学研究科, 数学, Japan
- - 1986, Osaka University, Graduate School, Division of Natural Science
- - 1981, Osaka University, School of Science, 数学, Japan
- - 1981, Osaka University, Faculty of Science

A distance on the equivalence classes of spherical curves generated by deformations of type RI

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'])., WORLD SCIENTIFIC PUBL CO PTE LTD, Oct. 2018, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 27 (12), doi;web_of_scienceScientific journal

The growth rate of the tunnel number of m-small knots

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., University of California, Berkeley, 2018, Pacific Journal of Mathematics, 295 (1), 57 - 101, doiScientific journal

THE SPECTRUM OF THE GROWTH RATE OF THE TUNNEL NUMBER IS INFINITE

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., AMER MATHEMATICAL SOC, Aug. 2016, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 144 (8), 3609 - 3618, doi;web_of_scienceScientific journal

A knot with destabilized bridge spheres of arbitrarily high bridge number

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., OXFORD UNIV PRESS, Apr. 2016, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 93, 379 - 396, doi;web_of_scienceScientific journal

Bridge splittings of links with distance exactly n

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., ELSEVIER SCIENCE BV, Dec. 2015, TOPOLOGY AND ITS APPLICATIONS, 196, 608 - 617, doi;web_of_scienceScientific journal

STRONG CYLINDRICALITY AND THE MONODROMY OF BUNDLES

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., AMER MATHEMATICAL SOC, Jul. 2015, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 143 (7), 3169 - 3176, doi;web_of_scienceScientific journal

Hyperbolic volume and Heegaard distance

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., INT PRESS BOSTON, INC, Mar. 2014, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 22 (2), 247 - 268, doi;web_of_scienceScientific journal

Heegaard splittings of distance exactly n

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., GEOMETRY & TOPOLOGY PUBLICATIONS, 2014, ALGEBRAIC AND GEOMETRIC TOPOLOGY, 14 (3), 1395 - 1411, doi;web_of_scienceScientific journal

(1,1)-bridge splitting with distance exactly n,

2013, RIMS Kokyuroku, 1868, 32--37A linear bound on the tetrahedral number of manifolds of bounded volume (after Jorgensen and Thurston)

AMER MATHEMATICAL SOC, 2011, TOPOLOGY AND GEOMETRY IN DIMENSION THREE: TRIANGULATIONS, INVARIANTS, AND GEOMETRIC STRUCTURES, 560, 27 - +, web_of_scienceInternational conference proceedings

Destabilizing Heegaard splittings of knot exteriors

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., ELSEVIER SCIENCE BV, Jan. 2010, TOPOLOGY AND ITS APPLICATIONS, 157 (1), 202 - 212, doi;web_of_scienceScientific journal

A design for pseudo-Anosov braids using hypotrochoid curves

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,, ELSEVIER SCIENCE BV, Jan. 2010, TOPOLOGY AND ITS APPLICATIONS, 157 (1), 280 - 289, doi;web_of_scienceScientific journal

Manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings

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., INT PRESS BOSTON, INC, Oct. 2009, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 17 (4), 637 - 649, web_of_scienceScientific journal

Knots with g(E(K))=2 and g(E(K # K # K))=6 and Morimoto's Conjecture

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., ELSEVIER SCIENCE BV, Mar. 2009, TOPOLOGY AND ITS APPLICATIONS, 156 (6), 1114 - 1117, doi;web_of_scienceScientific journal

The amalgamation of high distance Heegaard splittings is always efficient

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., SPRINGER, Jul. 2008, MATHEMATISCHE ANNALEN, 341 (3), 707 - 715, doi;web_of_scienceScientific journal

Seifert surfaces in open books, and a new coding algorithm for links

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., OXFORD UNIV PRESS, Jun. 2008, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 40 (3), 405 - 414, doi;web_of_scienceScientific journal

Knot exteriors with additive Heegaard genus and Morimoto's Conjecture

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]., GEOMETRY & TOPOLOGY PUBLICATIONS, 2008, ALGEBRAIC AND GEOMETRIC TOPOLOGY, 8 (2), 953 - 969, doi;web_of_scienceScientific journal

Heegaard genus of the connected sum of m-small knots

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]., INT PRESS CO LTD, Dec. 2006, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 14 (5), 1037 - 1077, web_of_scienceScientific journal

On the growth rate of the tunnel number of knots

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., WALTER DE GRUYTER & CO, 2006, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 592, 63 - 78, doi;web_of_scienceScientific journal

A search method for thin positions of links

We give a method for searching for thin positions of a given link., GEOMETRY & TOPOLOGY PUBLICATIONS, 2005, ALGEBRAIC AND GEOMETRIC TOPOLOGY, 5, 1027 - 1050, web_of_scienceScientific journal

Separating incompressible surfaces and stabilizations of Heegaard splittings

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., CAMBRIDGE UNIV PRESS, Nov. 2004, MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 137, 633 - 643, doi;web_of_scienceScientific journal

Local detection of strongly irreducible Heegaard splittings via knot exteriors

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., ELSEVIER SCIENCE BV, Mar. 2004, TOPOLOGY AND ITS APPLICATIONS, 138 (1-3), 239 - 251, doi;web_of_scienceScientific journal

Scharlemann-Thompson untelescoping of Heegaard splittings is finer than Casson-Gordon's

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., WORLD SCIENTIFIC PUBL CO PTE LTD, Nov. 2003, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 12 (7), 877 - 891, doi;web_of_scienceScientific journal

Locally Thin Position for a Link(共著)

2003, Kobe J. Math., 20, 1 - 10Heegaard splittings of exteriors of two bridge knots

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., GEOMETRY & TOPOLOGY PUBLICATIONS, 2001, GEOMETRY & TOPOLOGY, 5, 609 - 650, web_of_scienceScientific journal

Pre-taut sutured manifolds and essential laminations

OSAKA JOURNAL OF MATHEMATICS, Dec. 2001, OSAKA JOURNAL OF MATHEMATICS, 38 (4), 905 - 922, web_of_scienceScientific journal

The Rubinstein-Scharlemann graphic of a 3-manifold as the discriminant set of a stable map

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., PACIFIC JOURNAL MATHEMATICS, Sep. 2000, PACIFIC JOURNAL OF MATHEMATICS, 195 (1), 101 - 156, web_of_scienceScientific journal

Classification of unknotting tunnels for two bridge knots

1999, Geometry and Topology Monographs, 2, 259 - 290Essential tangle decomposition from thin position of a link

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)., PACIFIC JOURNAL MATHEMATICS, May 1997, PACIFIC JOURNAL OF MATHEMATICS, 179 (1), 101 - 117, web_of_scienceScientific journal

On canonical genus and free genus of knot

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., WORLD SCIENTIFIC PUBL CO PTE LTD, Feb. 1996, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 5 (1), 77 - 85, web_of_scienceScientific journal

Example of hyperbolic knot which do not admit depth 1 foliation

1996, Kobe Journal of Mathematics, 13, 209 - 221A NECESSARY AND SUFFICIENT CONDITION FOR A 3-MANIFOLD TO HAVE GENUS-G HEEGAARD SPLITTING (A PROOF OF HASS-THOMPSON CONJECTURE)

OSAKA JOURNAL OF MATHEMATICS, Mar. 1994, OSAKA JOURNAL OF MATHEMATICS, 31 (1), 109 - 136, web_of_scienceScientific journal

A construction of arbitrarily high degeneration of tunnel numbers of knots under connected sum

1994, Journal of knot theory and its ramification, 3, 179 - 186Knots which are prime on band connected sum

1994, Proc. Applied Math. Workshop KAIST, 4, 79 - 89A CONSTRUCTION OF 3-MANIFOLDS WHOSE HOMEOMORPHISM CLASSES OF HEEGAARD-SPLITTINGS HAVE POLYNOMIAL-GROWTH

OSAKA JOURNAL OF MATHEMATICS, Dec. 1992, OSAKA JOURNAL OF MATHEMATICS, 29 (4), 653 - 674, web_of_scienceScientific journal

Fibered links which are band connected sum of two links

1992, Knots 90, 9 - 23A CRITERION FOR DETECTING INEQUIVALENT TUNNELS FOR A KNOT

CAMBRIDGE UNIV PRESS, May 1990, MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 107, 483 - 491, web_of_scienceScientific journal

FIBERED LINKS AND UNKNOTTING OPERATIONS

OSAKA JOURNAL OF MATHEMATICS, Dec. 1989, OSAKA JOURNAL OF MATHEMATICS, 26 (4), 699 - 742, web_of_scienceScientific journal

UNIQUENESS OF MINIMAL GENUS SEIFERT SURFACES FOR LINKS

ELSEVIER SCIENCE BV, Nov. 1989, TOPOLOGY AND ITS APPLICATIONS, 33 (3), 265 - 279, web_of_scienceScientific journal

GENERALIZED UNKNOTTING OPERATIONS AND TANGLE DECOMPOSITIONS

AMER MATHEMATICAL SOC, Feb. 1989, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 105 (2), 471 - 478, web_of_scienceScientific journal

Minimal genus Seifert surfaces for unknotting number 1 knots

1989, Kobe J. Math., 6, 53 - 62CASSON-GORDON RECTANGLE CONDITION OF HEEGAARD DIAGRAMS AND INCOMPRESSIBLE TORI IN 3-MANIFOLDS

OSAKA JOURNAL OF MATHEMATICS, Sep. 1988, OSAKA JOURNAL OF MATHEMATICS, 25 (3), 553 - 573, web_of_scienceScientific journal

Heights of simple loops and pseudo-Anosov homeomorphisms

1988, Contemporary math., 78, 327 - 338CYCLOTOMIC INVARIANTS FOR LINKS

JAPAN ACAD, Sep. 1988, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 64 (7), 235 - 238, web_of_scienceScientific journal

PSEUDO-ANOSOV HOMEOMORPHISMS WHICH EXTEND TO ORIENTATION REVERSING HOMEOMORPHISMS OF S3

OSAKA JOURNAL OF MATHEMATICS, Dec. 1987, OSAKA JOURNAL OF MATHEMATICS, 24 (4), 739 - 743, web_of_scienceScientific journal

STRUCTURES OF FULL HAKEN MANIFOLDS

OSAKA JOURNAL OF MATHEMATICS, Mar. 1987, OSAKA JOURNAL OF MATHEMATICS, 24 (1), 173 - 215, web_of_scienceScientific journal

HOMEOMORPHISMS OF 3-MANIFOLDS AND TOPOLOGICAL-ENTROPY

OSAKA JOURNAL OF MATHEMATICS, 1985, OSAKA JOURNAL OF MATHEMATICS, 22 (2), 289 - 297, web_of_scienceScientific journal

LINKS OF HOMEOMORPHISMS OF A DISK AND TOPOLOGICAL-ENTROPY

SPRINGER VERLAG, 1985, INVENTIONES MATHEMATICAE, 80 (1), 153 - 159, web_of_scienceScientific journal

PRIMITIVE LINKS OF NON-SINGULAR MORSE-SMALE FLOWS ON THE SPECIAL SEIFERT FIBERED MANIFOLDS

ELSEVIER SCIENCE BV, 1985, TOPOLOGY AND ITS APPLICATIONS, 20 (1), 67 - 78, web_of_scienceScientific journal

On 3-manifolds with no periodic maps(共著)

1984, Japan J. Math., 10, 185--193NON-SEPARATING INCOMPRESSIBLE TORI IN 3-MANIFOLDS

MATH SOC JAPAN, 1984, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 36 (1), 11 - 22, web_of_scienceScientific journal

3-MANIFOLDS WHICH CONTAIN NONPARALLEL PROJECTIVE-PLANES

AMER MATHEMATICAL SOC, 1984, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 91 (2), 314 - 318, web_of_scienceScientific journal

LINKS OF HOMEOMORPHISMS OF SURFACES AND TOPOLOGICAL-ENTROPY

JAPAN ACAD, 1984, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 60 (10), 381 - 383, web_of_scienceScientific journal

STRUCTURES OF THE HAKEN MANIFOLDS WITH HEEGAARD-SPLITTINGS OF GENUS-2

OSAKA JOURNAL OF MATHEMATICS, 1984, OSAKA JOURNAL OF MATHEMATICS, 21 (2), 437 - 455, web_of_scienceScientific journal

EQUIVARIANT ANNULUS THEOREM FOR 3-MANIFOLDS

JAPAN ACAD, 1983, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 59 (8), 403 - 406, web_of_scienceScientific journal

On keen Heegaard splittings

Oct. 2018, Adv. Stud. Pure Math., 78, 293 - 311

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, 2007Realizing 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, 2007Links 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., 1984Links 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

折り紙に現れる幾つかの数学構造について

トポロジーとコンピュータ, 2017Complexes induced from spherical curves and distances

結び目の数学X, 2017折り紙の数学入門

Knotting Nagoya, 2016A construction of flat-foldable origami via similarity structure

Low dimensional topology and number theory VII, 2015A construction of flat-foldable origami via similarity structure

Low dimensional topology and number theory VII, 2015On keen Heegaard splitting

Topology and Geometry of Low-dimensional Manifolds, 2014On keen Heegaard splitting

Topology and Geometry of Low-dimensional Manifolds, 20142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

Spring Workshop 2013 on Low-Dimensional Topology and its Ramifications, 2013Heegaard splittings of distance $n$(joint work with Ayako Ido and Yeonhee Jang)

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）, 2013A construction of generaliza Mirura folding via similarity structure on 2-dimensional torus

Spring Workshop 2013 on Low-Dimensional Topology and its Ramifications, 2013Heegaard splittings of distance $n$(joint work with Ayako Ido and Yeonhee Jang)

International Conference on Topology and Geometry 2013 Joint with the 6th Japan-Mexico Topology Symposium, 2013Heegaard splitting with distance exactly n for each non-negative integer n

日大トポロジーセミナー, 2012On the growth rate of tunnel numbers of knots

Workshop on Low Dimensional Topology in Shanghai and Suzhou, 2011On the growth rate of tunnel numbers of knots

Workshop on Low Dimensional Topology in Shanghai and Suzhou, 2011Toward Haken type theorems for essential laminations in 3-manifolds: Proposal of fundamental settings and applications

E-KOOKセミナー2010, 2010Realization problems of distances of Heegaard splittings

Simplicial Complexes Arising in Low-Dimensional Topology, 2009On thin presentations of 3-manifolds and links

Category Theory, Computer Science, and Topology, 2009