講 演 者 ：門田 直之 (京都大学) タ イ ト ル ：On stable commutator length of a Dehn twist （アブストラクト） (PDF) 日 時 ：2月1日（金）16：00～17：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：小畑 久美 (大阪市立大学数学研究所(OCAMI)) タ イ ト ル ：On enumeration of edge colored graphs (joint work withYasuo Ohno (Kinki University)) （アブストラクト） (PDF) 日 時 ：2月1日（金）15：00～16：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：張 娟姫 (奈良女子大学) タ イ ト ル ：Heegaard splittings of distance $n$ （アブストラクト） (PDF) 日 時 ：1月25日（金）16：00～17：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：清水 理佳 (広島大学) タ イ ト ル ：The reducivity of spherical curves （アブストラクト） (PDF) 日 時 ：12月14日（金）16：00～17：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：Cheng Zhiyun (Beijing Normal University) タ イ ト ル ：A polynomial invariant of virtual knots and links （アブストラクト） (PDF) 日 時 ：12月7日（金）16：00～17：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：Sang Youl Lee (Pusan National University) タ イ ト ル Studying knots and links via net diagrams （アブストラクト） (PDF) 日 時 ：11月30日（金）16：10～17：10 場 所 数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：Jieon Kim (Pusan National University) タ イ ト ル ：The Alexander biquandles for oriented surface links （アブストラクト） (PDF) 日 時 ：11月30日（金）15：30～16：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：Yewon Joung (Pusan National University) タ イ ト ル ：Obstructions for Yoshikawa's moves on marked graph diagrams for surface links （アブストラクト） (PDF) 日 時 ：11月30日（金）15：00～15：30 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：早野 健太 (大阪大学) タ イ ト ル ：Vanishing cycles and homotopies of wrinkled fibrations （アブストラクト） (PDF) 日 時 ：11月9日（金）16：00～17：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：岡崎 建太（京都大学数理解析研究所(RIMS)） タ イ ト ル ：On the state-sum invariants of 3-manifolds constructed from the E_6 and E_8 linear skeins （アブストラクト） (PDF) 日 時 ：11月2日（金）16：00～17：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：森 淳秀 (大阪市立大学数学研究所) タ イ ト ル ：Essential dichotomy in contact topology （アブストラクト） (PDF) 日 時 ：11月2日（金）15：00～16：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：岡崎 真也(大阪市立大学数学研究所) タ イ ト ル ：Bridge genus and braid genus of lens space （アブストラクト） (PDF) 日 時 ：10月26日（金）16：00～17：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：石井 敦 (筑波大学) タ イ ト ル ：On some properties of handlebody-knots （アブストラクト） (PDF) 日 時 ：10月19日（金）16：00～17：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：Javier Arsuaga (San Francisco State University) タ イ ト ル ：Using knot theory to model the formation of minicircle networks on trypanosomatida （アブストラクト） (PDF) 日 時 ：10月19日（金）15：00～16：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：門上 晃久 (East China Normal University) タ イ ト ル ：Switching scheme and switching complex （アブストラクト） (PDF) 日 時 ：10月5日（金）16：00～17：00 場 所 ：数学　第3セミナー室（共通研究棟4階401室） Top 講 演 者 ：Michael Yoshizawa（University of California, Santa Barbara） タ イ ト ル ：Generating Examples of High Distance Heegaard Splittings （アブストラクト） (PDF) 日 時 ：7月20日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：Greg McShane（Universite Joseph Fourier） タ イ ト ル ：Orthospectra and identities （アブストラクト） (PDF) 日 時 ：7月13日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：矢口 義朗（群馬工業高等専門学校） タ イ ト ル ：On the extended 1-st Johnson homomorphism of the braid group （アブストラクト） (PDF) 日 時 ：7月13日（金）15：00～16：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：鈴木 咲衣 （京都大学数理解析研究所(RIMS)） タ イ ト ル ：Bing doubling and the colored Jones polynomials （アブストラクト） (PDF) 日 時 ：7月6日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：屋代 司 （Sultan Qaboos University） タ イ ト ル ：On surface-knots with cross-exchangeable cycles （アブストラクト） (PDF) 日 時 ：7月6日（金）15：00～16：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：三浦 嵩広 （神戸大学） タ イ ト ル ：On the flat braidzel length of links （アブストラクト） (PDF) 日 時 ：6月29日（金）15：00～16：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：鎌田 直子（名古屋市立大学） タ イ ト ル ：Surface bracket polynomials of twisted links （アブストラクト） (PDF) 日 時 ：6月22日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：安部 哲哉（京都大学数理解析研究所(RIMS)） タ イ ト ル ：The knot 12a990 is ribbon （アブストラクト） (PDF) 日 時 ：6月15日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：田山 育男 (大阪市立大学数学研究所) タ イ ト ル ：Tabulation of 3-manifolds of lengths up to 10 （アブストラクト） (PDF) 日 時 ：6月8日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：能城 敏博 (大阪市立大学数学研究所) タ イ ト ル ：On extendibility of a map induced by Bers isomorphism （アブストラクト） (PDF) 日 時 ：6月1日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：野坂 武史 (京都大学数理解析研究所 / 日本学術振興会特別研究員PD) タ イ ト ル ：Mochizuki's quandle 3-cocycles and Inoue-Kabaya chain map （アブストラクト） (PDF) 日 時 ：5月25日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：清水 理佳 (広島大学) タ イ ト ル ：The half-twisted splice operation on reduced knot projections （アブストラクト） (PDF) 日 時 ：5月11日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：門上 晃久 (East China Normal University) タ イ ト ル ：Integrality of Seifert surgery coefficient of twist knot, and Reidemeister torsion (joint work with Tsuyoshi Sakai (Nihon University)) （アブストラクト） (PDF) 日 時 ：4月27日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top 講 演 者 ：Chad Musick（名古屋大学） タ イ ト ル ：Drawing Minimal Bridge Projections of Links （アブストラクト） (PDF) 日 時 ：4月20日（金）16：00～17：00 場 所 ：数学　第3セミナー室（3153） Top

講 演 者：	門田 直之 (京都大学)
タ イ ト ル：	On stable commutator length of a Dehn twist

Let $[G,G]$ be the commutator subgroup of a group $G$. For $x\in [G,G]$, we will denote by ${\rm cl}(x)$ the smallest number of commutators in G whose product is equal to $x$. We call ${\rm cl}(x)$ the commutator length of $x$. The stable commutator length of $x$, denoted by ${\rm scl}(x)$, is the limit $${\rm scl}(x)=\lim_{n\rightarrow \intfy}\frac{{\rm cl}(x^n)}{n}.$$ In generally, computing (stable) commutator length is difficult. In this talk, we will present some background results of stable commutator length in mapping class groups. And we will give an upper bound of the stable commutator length of a Dehn twist. This is joint work with Danny Calegari and Masatoshi Sato.

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講 演 者：	小畑 久美 (大阪市立大学数学研究所(OCAMI))
タ イ ト ル：	On enumeration of edge colored graphs (joint work with Yasuo Ohno (Kinki University))

We previously gave a generalization of Ohno's theorem which gives a formula for enumeration of cyclic automorphism graphs. We analogously consider the enumeration of edge colored graphs under transposition.

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講 演 者：	張 娟姫 (奈良女子大学)
タ イ ト ル：	Heegaard splittings of distance $n$

Hempel introduced the concept of distance of Heegaard splitting by using curve complex, and showed that there exist Heegaard splittings of closed orientable 3-manifolds with distance $>n$ for any integer $n$. In this talk, we construct pairs of curves with distance exactly $n$ for any non-negative integer $n$, and use them to show that there exist Heegaard splittings of 3-manifolds with distance exactly $n$.
(This is a joint work with Ayako Ido and Tsuyoshi Kobayashi.)

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講 演 者：	清水 理佳 (広島大学)
タ イ ト ル：	The reducivity of spherical curves

We show that we can obtain a reducible spherical curve from any non-trivial spherical curve by three or less inverse-half-twisted splices, i.e., the reducivity, which represents how reduced a spherical curve is, is three or less. We also discuss some unavoidable sets of tangles for spherical curves.

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講 演 者：	Cheng Zhiyun (Beijing Normal University)
タ イ ト ル：	A polynomial invariant of virtual knots and links

Virtual knot theory was introduced by Professor Louis Kauffman in 1990s. One simple invariant of virtual knots, the odd writhe was defined by Kauffman himself in 2004. I will discuss the generalization of this invariant with two viewpoints: one comes from V. O. Manturov's parity axioms, the other approach was inspired by Professor Akio Kawauchi and Ayaka
Shimizu's warping polynomial. If time permits, I will also give a similar generalization of the linking number of 2-component links.

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講 演 者：	Sang Youl Lee (Pusan National University)
タ イ ト ル：	Studying knots and links via net diagrams

A net diagram is a knot or link diagram obtained from a quasitoric braid diagram by replacing each positive (respectively, negative) crossing with positive (respectively, negative) half-twists. Due to some recent works, net diagrams for knots and links turned out to have various ramifications and applications to study invariants for knots and links, including the Casson invariant, genus, delta unknotting number, Alexander polynomial, Jones polynomial and so on. In this talk, we will discuss some recent contributions towards MFW inequality and the Jones conjecture on a minimal braid representation, the Tripp conjecture on the canonical genus for Whitehead doubles of alternating knots and the Hoste's conjecture on the Alexander polynomial of alternating knots via net diagrams.
This is partly a joint work with H. J. Jang and M. Seo.

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講 演 者：	Jieon Kim (Pusan National University)
タ イ ト ル：	The Alexander biquandles for oriented surface links

A biquandle is an algebraic structure consisting of a set with four binary operations satisfying axioms derived from the oriented Reidemeister moves, where generators of the algebra are identified with semi-arcs in an oriented link diagram. This relationship between the biquandle axioms and the Reidemeister moves makes biquandles a natural source of (virtual) knot and link invariants. The Alexander biquandle is an example of a biquandle that gives rise to the generalized Alexander polynomial for oriented virtual knots and links. In this talk, we will discuss a construction of the Alexander biquandle for oriented surface links via marked graph diagrams. We will show that the elementary ideals for a presentation matrix for the biquandle are invariants for the oriented surface link. To do this we first give a minimal generating set of Yoshikawa's moves and then investigate the behavior of presentation matrices under Yoshikawa's moves. We also compute the invariants for oriented surface links represented by marked graph diagrams with triangle-type and square-type ch-graphs.
This is a joint work with Y. Joung and S. Y. Lee.

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講 演 者：	Yewon Joung (Pusan National University)
タ イ ト ル：	Obstructions for Yoshikawa's moves on marked graph diagrams for surface links

A surface link is a closed, possibly orientable or nonorientable, surface F smoothly embedded in the oriented 4-space R^4 or S^4. If F is a connected surface, then it is called a surface knot. If F is oriented, then we call it an oriented surface link. A surface link can be represented by a marked graph diagram, that is, a knotted regular 4-valence rigid vertex graph diagram in which each 4-valence vertex has a marker. Two marked graph diagrams represent the same surface link if and only if they are transformed into each other by a finite sequence of Yoshikawa's moves. In this talk, we will discuss some obstructions for Yoshikawa's moves derived from a polynomial defined by a state model analogous to the Kauffman's state model for the Jones polynomial of classical knots and links, and calculated by using a skein relation based on marked graph diagrams. We also discuss some applications of these obstructions.
This is a joint work with J. Kim and S. Y. Lee.

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講 演 者：	早野 健太 (大阪大学)
タ イ ト ル：	Vanishing cycles and homotopies of wrinkled fibrations

Wrinkled fibrations are fibration structures on four-manifolds, which have been studied recently for the purpose of understanding some invariants of four-manifolds. In this talk, we will explain how vanishing cycles of wrinkled fibrations are changed by several homotopies. As an application, we also give new examples of surface diagrams of four-manifolds, which are combinatorial descriptions of four-manifolds introduced by Williams. Part of the results in this talk is joint-work with Stefan Behrens (The Max Plank Institute for Mathematics).

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講 演 者：	岡崎 建太（京都大学数理解析研究所(RIMS)）
タ イ ト ル：	On the state-sum invariants of 3-manifolds constructed from the E_6 and E_8 linear skeins

The state-sum invariants of 3-manifolds, introduced by Turaev and Viro and generalized by Ocneanu, are formulated as a state-sum on triangulations of 3-manifolds derived from certain 6j-symbols. In this talk, we give elementary and self-contained constructions of the state-sum invariants of 3-manifolds derived from 6j-symbols of the E_6 and E_8 subfactors. We give such constructions by introducing E_6 and E_8 linear skeins, motivated by the E_6 and E_8 planar algebras.

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講 演 者：	森 淳秀 (大阪市立大学数学研究所)
タ イ ト ル：	Essential dichotomy in contact topology

A contact structure is a completely non-integrable hyperplane field usually defined by a global Pfaff equation. However, in saying so, I suspect that
1) three dimensional contact topology is just a three dimensional topology for an imaginary person who does not know a mirror, and
2) higher dimensional contact topology is just an analogue of three dimensional contact topology.
Indeed a contact structure fixes the orientation of the manifold even locally, while it has no moduli even globally. (A person who knows a mirror must wonder about the fact that two closed braids present the same contact knot iff they are related by only right-handed stabilizations/destabilizations.)
Though a 3-manifold admits infinitely many contact structures, most of them (i.e., overtwisted ones) are spoiled and uniquely determined by homotopy data of plane fields. Contrastingly, the topology of the other decent structures (i.e., tight ones) adds a few extra data to the topology of the 3-manifold itself.
I will talk about this dichotomy (overtwisted vs. tight) and its tentative generalizations.

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講 演 者：	岡崎 真也(大阪市立大学数学研究所)
タ イ ト ル：	Bridge genus and braid genus of lens space

The bridge genus and the braid genus are invariants of an oriented closed connected $3$-manifold which are introduced by Kawauchi. In this talk, we calculate the bridge genus and braid genus for some lens spaces $L(p,q)$, and we give an upper bound of $L(p,q)$ such that $p$ is an even number.

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講 演 者：	石井 敦 (筑波大学)
タ イ ト ル：	On some properties of handlebody-knots

A handlebody-knot is a handlebody embedded in the 3-sphere, and a handlebody-link is a disjoint union of handlebodies embedded in the 3-sphere. Two handlebody-links are equivalent if one can be transformed into the other by an isotopy of the 3-sphere. I will explain the basics of handlebody-knots, which include fundamental moves on diagrams. Then I will talk about some properties of handlebody-knots. This talk consists of short topics.

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講 演 者：	Javier Arsuaga (San Francisco State University)
タ イ ト ル：	Using knot theory to model the formation of minicircle networks on trypanosomatida

Trypanosomatida parasites, such as trypanosoma and lishmania, are the cause of deadly diseases in many third world countries. A distinctive feature of these organisms is the three dimensional organization of their mitochondrial DNA into maxi and minicircles. In some of these organisms minicircles are confined into a small disk shaped volume and are topologically linked, forming a gigantic linked network. The origins of such a network as well as of its topological properties are mostly unknown. In this paper we quantify the effects of the confinement on the topology of such a minicircle network. We introduce a simple mathematical model in which a collection of randomly oriented minicircles are spread over a rectangular grid. We present analytical and computational results showing that a positive critical percolation density exists, that the probability of formation of a highly linked network increases exponentially fast when minicircles are confined, and that the mean minicircle valence (the number of minicircles that a particular minicircle is linked to) increases linearly with density. When these results are interpreted in the context of the mitochondrial DNA of the trypanosome they suggest that confinement plays a key role on the formation of the linked network. This hypothesis is supported by the agreement of our simulations with experimental results that show that the valence grows linearly with density. Our model predicts the existence of a percolation density and that the distribution of minicircle valences is more heterogeneous than initially thought.

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講 演 者：	門上 晃久 (East China Normal University)
タ イ ト ル：	Switching scheme and switching complex

Motivated by a notion, region crossing change, which is defined by A.
Shimizu, we define generalized notions, switching scheme and switching complex.

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講 演 者：	Michael Yoshizawa（University of California, Santa Barbara）
タ イ ト ル：	Generating Examples of High Distance Heegaard Splittings

Given a closed orientable 3-manifold M, a surface S in M is a Heegaard surface if it separates the manifold into two handlebodies of equal genus. This decomposition is called a Heegaard splitting of M. The Hempel distance of this splitting is the length of the shortest path in the curve complex of S between the disk complexes of the two handlebodies. In 2004, Evans developed an iterative process to construct a manifold that admits a Heegaard splitting with arbitrarily high distance. We first provide an introduction to Heegaard splittings and Hempel distance and then improve on Evans' results.

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講 演 者：	Greg McShane（Universite Joseph Fourier）
タ イ ト ル：	Orthospectra and identities

The orthospectra of a hyperbolic manifold with geodesic boundary consists of the lengths of all geodesics perpendicular to the boundary. We discuss the properties of the orthospectra, asymptotics, multiplicity and identities due to Basmajian, Bridgeman and Calegari. We will give a proof that the identities of Bridgeman and Calegari are the same.

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講 演 者：	矢口 義朗（群馬工業高等専門学校）
タ イ ト ル：	On the extended 1-st Johnson homomorphism of the braid group

The braid group $B_m$ of degree $m$ is regarded as a mapping class group $M(D_m)$ of the $m$-puncterd disk $D_m$. There exists a natural surjective homomorphism from $B_m$ to the symmetric group $S_m$ of degree $m$, which is regarded as a homomorphism from $M(D_m)$ to the automorphism group of the 1-st homology group $H_1(D_m)$. By using an analogy of the Johnson's theory for mapping class groups of compact oriented surfaces, we construct a homomorphism from $B_m$ to a group extension of $S_m$. We call it the extended 1-st Jhonson homomorphism of $B_m$. We also study a way to caluculate the extended 1-st Johnson homomorphism by using braid diagrams. This is a joint work with Yusuke Kuno.

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講 演 者：	鈴木 咲衣 （京都大学数理解析研究所(RIMS)）
タ イ ト ル：	Bing doubling and the colored Jones polynomials

The colored Jones polynomial is a quantum invariant associated with the quantized enveloping algebra of the Lie algebra sl2. We are interested in the relationship between topological properties of links and algebraic properties of the colored Jones polynomial. Bing doubling is an operation which gives a satellite of a knot. Habiro defined a certain series of the colored Jones polynomials to construct the unified WRT invariant of 3-manifolds. In this talk, we derive Habiro's colored Jones polynomials of the Bing double of a knot K from these of K. We aim to apply the result to study the unified WRT invariant.

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講 演 者：	屋代 司 （Sultan Qaboos University）
タ イ ト ル：	On surface-knots with cross-exchangeable cycles

A surface-knot is a closed oriented surface embedded in 4-space. A surface diagram of a surface-knot is the projected image in 3-space under the orthogonal projection with crossing information. It is not known whether or not any surface diagram can be obtained from a trivial surface diagram by applying crossing changes along double curves. For some surface diagrams, there exist special double curves along which crossing information can be changed so that the surface diagram is deformed into a trivial surface diagram. In this talk, we present a construction to obtain a family of surface-knots with exchangeable cycles. This research consists of collaboration projects with A. Mohamad and also with A. AlKharusi.

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講 演 者：	三浦 嵩広 （神戸大学）
タ イ ト ル：	On the flat braidzel length of links

It is known that any link has a flat braidzel surface as a Seifert surface. We introduce the flat braidzel length of a link defined as the minimal length of all braids which represent flat braidzel surfaces for the link. In this talk, we study relationships between the flat braidzel length and the Alexander-Conway polynomial and give a lower bound for the flat braidzel length. If time allows, we will show that, for any integer n greater than or equal to three, there exists a knot whose flat braidzel length is n.

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講 演 者：	鎌田 直子（名古屋市立大学）
タ イ ト ル：	Surface bracket polynomials of twisted links

Bourgoin defined the notion of a twisted link. Twisted links are equivalent to abstract links on non-orientable surfaces. Dye and Kauffman defined the surface bracket polynomials of virtual links. In this talk I introduced those of twisted links. We discuss a relationship between the multivariable invariant and the surface bracket polynomials of twisted links.

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講 演 者：	安部 哲哉（京都大学数理解析研究所(RIMS)）
タ イ ト ル：	The knot 12a990 is ribbon

Herald, Kirk and Livingston showed that the knot 12a990 is slice. Indeed, they showed that the connected sum of 12a990 with T(2,3) and T(2,-3) is ribbon, where T(2,3) and T(2,-3) are right- and left-handed trefoils. We observe that 12a990 is ribbon and generalize this fact. The rest of the time, we study homotopically slice knots obtained from unknotting number one ribbon knots by applying annulus twists.
This is a joint work with In Dae Jong and Motoo Tange.

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講 演 者：	田山 育男 (大阪市立大学数学研究所)
タ イ ト ル：	Tabulation of 3-manifolds of lengths up to 10

This is a joint work with A. Kawauchi.
A well-order was introduced on the set of links by A. Kawauchi. This well-order also naturally induces a well-order on the set of prime link groups and eventually induces a well-order on the set of closed connected orientable $3$-manifolds. With respect to this order, we enumerated the prime links, the prime link groups and 3-manifolds with lengths up to 10. In this talk, we show a list of the enumeration of $3$-manifolds and discuss a relationship between link exteriors and link groups.

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講 演 者：	能城 敏博 (大阪市立大学数学研究所)
タ イ ト ル：	On extendibility of a map induced by Bers isomorphism

Let $T(S)$ be the Teichmuller space of a closed Riemann surface $S$ of genus $g(>1)$. Denote by $U$ the universal covering of $S$, that is, the upper half-plane and denote by $\dot{S}$ the surface obtained by removing a point from $S$. By Bers isomorphism theorem, we have a map from $T(S) \times U$ to $T(\dot{S})$. It is known that the Teichmuller space $T(\dot{S})$ is embedded in $(3g-2)$-dimensional complex vector space. Thus the boundary $\partial T(\dot{S})$ of $T(\dot{S})$ is naturally defined.

Let $A$ be a subset of $\partial U$ consisting of all points filling $S$. In this talk, we show that the map of $T(S) \times U$ to $T(\dot{S})$ has a continuous extension of $T(S)\times (U \cup A)$ into $T(\dot{S}) \cup \partial T(\dot{S})$. This is a joint work with Hideki Miyachi (Osaka University).

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講 演 者：	野坂 武史 (京都大学数理解析研究所 / 日本学術振興会特別研究員PD)
タ イ ト ル：	Mochizuki's quandle 3-cocycles and Inoue-Kabaya chain map

In 2003, T. Mochizuki has determined the third quandle cohomologies of all Alexander quandles $X$ over finite fields; further he listed polynomials-presentations of their basis, as solutions of differential equations. I show that all the Mochizuki's 3-cocycles are derived from certain group 3-cohomologies via Inoue-Kabaya chain map. For example, if $X$ is the dihedral quandle, the Mochizuki's 3-cocycle is deduced with an easy computation.

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講 演 者：	清水 理佳 (広島大学)
タ イ ト ル：	The half-twisted splice operation on reduced knot projections

We show that any nontrivial reduced knot projection can be obtained from a trefoil projection by a finite sequence of half-twisted splice operations and their inverses without becoming a reducible projection. This is a joint work with Noboru Ito.

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講 演 者：	門上 晃久 (East China Normal University)
タ イ ト ル：	Integrality of Seifert surgery coefficient of twist knot, and Reidemeister torsion (joint work with Tsuyoshi Sakai (Nihon University))

M. Brittenham and Y. Wu determined exceptional surgeries along every $2$-bridge knot by using a lamination structure of the knot complement. In particular, a $2$-bridge knot producing Seifert fibered spaces is a twist knot, which is denoted by $C(2n, 2)$\ $(n\in \mathbb{Z})$ in Conway's notation up to mirror images, and its Seifert surgery coefficients are $1$, $2$ and $3$ (and more for $n=0, \pm 1$). The speaker proved that the Alexander polynomial of a twist knot for $n\ne 0, -1$ restricts the positive numerators of Seifert surgery coefficients into $1$, $2$ or $3$. We try to prove that the denominators of Seifert surgery coefficients are $\pm 1$ (i.e.\ integrality) by using the Alexander polynomial of the knot and an invariant deduced from the Reidemeister torsion of the branched covering over the knot. We obtained necessary conditions as Diophantine equations, and partial answers for some cases.

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講 演 者：	Chad Musick（名古屋大学）
タ イ ト ル：	Drawing Minimal Bridge Projections of Links

A method is given to achieve a minimal-bridge projection of a knot. This method relies on maze-solving and minimal path finding to shift all over-crossings off of extra underpasses. The method is proven correct by considering the knot as a fiber bundle from one end of a cylinder to the other end.

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