組織委員 岩切 雅英
| 日時 | 2010年2月12日（金）16：30～17：30 |
| 講演者（所属） | Mark Powell（University of Edinburgh） |
| タイトル | Knot Concordance and Twisted Blanchfield Forms |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | In this talk I will recall the notion of knot concordance as defined by
Fox and Milnor, which asks whether a knot in S3 bounds a disk in 4 space
D4. The work of Casson and Gordon involved a two stage obstruction theory
which depends on the intersection form of a 4-manifold. This has been generalised
by the work of Cochran-Orr-Teichner. I shall discuss an obstruction theory which is intrinsically 3-dimensional, using Blanchfield linking forms with coefficients twisted using metabelian representations of the knot group. These linking forms obstruct null-concordance. We then describe an algorithm to construct the symmetric chain complex of the universal cover of a knot exterior, and then use this to make calculations of the twisted Blanchfield forms. |
| 日時 | 2010年2月5日（金）16：00～17：00 |
| 講演者（所属） | 田中 心（東京学芸大学） |
| タイトル | A recent approach to the smooth 4-dimensional Poincare conjecture |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | We will report on the preprint (arXiv:0906.5177) written by M. Freedman, R. Gompf, S. Morrison and K. Walker. They proposed some strategies to disprove/prove the smooth 4-dimensional Poincare conjecture, which is called "SPC4" for short. In this talk, we mainly focus on one of their strategies to disprove SPC4 by using the Rasmussen invariant, which is a knot concordance invariant derived from (a variant of) the Khovanov homology theory. |
| 日時 | 2010年1月15日（金）16：00～17：00 |
| 講演者（所属） | 張 明星（大阪市立大学） |
| タイトル | Standard surfaces embedded in a genus 2 handlebody |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | In this talk, we will introduce some disks and annuli in a genus 2 handle body, which we call them standard. And the standard surfaces will help us know the incompressible surfaces in a knot complement. |
| 日時 | 2010年1月8日（金）16：00～17：00 |
| 講演者（所属） | 門上 晃久（大連理工大学） |
| タイトル | Alexander polynomials of algebraically split amphicheiral links (partially joint work with Akio Kawauchi) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | We provide necessary conditions for algebraically split links to be amphicheiral
by the Alexander polynomials of them. Firstly, we study algebraically split amphicheiral links only by using the Alexander polynomials. Secondly (this part is the joint work), we study them by using the signature invariants. |
| 日時 | 2009年12月4日（金）16：00～17：00 |
| 講演者（所属） | 梅田 早希（奈良女子大学） |
| タイトル | On topological methods for constructing efficient mixings |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | Topological nature of stirring fluid by using finitely many rods is closely related to Nielsen-Thurston theory and braid theory. It is natural to expect that stirrings corresponding to pseudo-Anosov braids can mix up fluid efficiently. Making use of this idea, various mixing devices are proposed by several authors, and their efficiencies are confirmed by using computer simulations and experiments. In this talk, we introduce other mixing device with simple structures consisting of few gears, where the movements of the rods are hypotrochoid curves. We show that the braid corresponding to the movement is pseudo-Anosov type by using linking numbers of the closure of it and covering space. We believe that our device has an advantage for practical use from the viewpoint of the efficiency of the mixings. |
| 日時 | 2009年11月27日（金）16：00～17：00 |
| 講演者（所属） | 金信 泰造（大阪市立大学） |
| タイトル | $H(2)$-Gordian Distance of Knots |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | An $H(2)$-move is a local move of a knot, which is performed by adding a half-twisted band. It is known an $H(2)$-move is an unknotting operation. We define the $H(2)$-{Gordian distance} of two knots to be the minimum number of $H(2)$-moves needed to transform one into the other. We give several methods to estimate the $H(2)$-Gordian distance of knots; many of them are generalizations of the methods used to estimate an $H(2)$-unknotting number. Then we give a table of $H(2)$-Gordian distances of knots with up to $7$ crossings. |
| 日時 | 2009年11月20日（金）16：00～17：00 |
| 講演者（所属） | 安井 弘一（京都大学数理解析研究所） |
| タイトル | On corks of 4-manifolds (joint work with Selman Akbulut) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | It is known that every exotic smooth structure on a simply connected closed 4-manifold is determined by a codimention zero compact contractible submanifold and an involution on the boundary. Such a pair is called a cork. In this talk, we give various examples of cork structures of 4-manifolds. |
| 日時 | 2009年11月6日（金）16：00～17：00 |
| 講演者（所属） | 森内 博正（OCAMI） |
| タイトル | An enumeration of non-prime theta-curves and handcuff graphs with up to seven crossings |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | We have enumerated all the prime theta-curves and handcuff graphs with up to seven crossings before. We can composite many spatial graphs by using ``connected sum'' of them. However, for spatial graphs, ``connected sum'' is not unique. In this talk, we enumerate non-prime theta-curves and handcuff graphs with up to seven crossings by using algebraic tangles and non-prime basic theta-polyhedra. |
| 日時 | 2009年10月30日（金）16：00～17：00 |
| 講演者（所属） | 大城 佳奈子（広島大学） |
| タイトル | Cocycle invariants with quandles and symmetric doubles for oriented links |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | Quandle cocycle invariants are introduced for oriented (classical or surface)
links and they are usefully applied for several studies of classical links
and orientable surface-links. On the other hand, symmetric quandle cocycle
invariants were introduced as a quandle invariant for all classical links
and surface-links. However, by the construction of symmetric quandle homology
groups and knot invariants, it is expected that the symmetric quandle invariants
are weaker than the quandle invariants for oriented links. Is it ture? In this talk, we give the answer. |
| 日時 | 2009年10月23日（金）16：00～17：00 |
| 講演者（所属） | 花木 良（早稲田大学） |
| タイトル | On intrinsically knotted or completely 3-linked graphs (joint work with Ryo Nikkuni, Kouki Taniyama and Akiko Yamazaki) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | It is known that the graphs obtained from $K_7$ by Delta-Y moves are intrinsically
knotted. Flapan and Naimi showed that there exists a graph obtained from $K_7$ by Delta-Y moves and Y-Delta moves which is not intrinsically knotted. We show that the graphs obtained from $K_7$ by Delta-Y moves and Y-Delta moves are intrinsically knotted or completely 3-linked. Here a graph is said to be intrinsically knotted or completely 3-linked if every embedding of the graph in $R3$ contains a nontrivial knot or a 3-component link each of whose 2-component sublink is nonsplittable. |
| 日時 | 2009年10月9日（金）16：00～17：00 |
| 講演者（所属） | 蒲谷 祐一（OCAMI） |
| タイトル | A complex volume formula via quandle shadow coloring (joint work with Ayumu Inoue) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | For a hyperbolic manifold M, Vol(M) + i CS(M) is called the complex volume
of M where Vol(M) and CS(M) are volume and Chern-Simons invariant of M
respectively. W. Neumann defined the extended Bloch group \hat{B}(C) and gave a formula of the complex volume using \hat{B}(C). In this talk, we introduce a construction of the element of extended Bloch group from the quandle 2-cycle associated with a shadow coloring. Combined with works of Neumann and Dupont-Zickert, we obtain a formula of complex volume. This is a joint work with Ayumu Inoue (Tokyo Institute of Technology). |
| 日時 | 2009年10月2日（金）16：00～17：00 |
| 講演者（所属） | 岩切 雅英（OCAMI） |
| タイトル | Surface-links represented by 4-charts and quandle cocycle invariants |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | Any surface-link can be deformed into the closure of a surface braid of some degree $m$ and can be also represented by an $m$-chart. In this talk, we will study the surface-links represented by $4$-charts and their quandle cocycle invariant, and show the result related to the $w$-index of surface links. |
| 日時 | 2009年7月24日（金）16：00～17：00 |
| 講演者（所属） | 鈴木 咲衣（京都大学数理解析研究所） |
| タイトル | On the universal $sl_2$ invariant of ribbon bottom tangles |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | A bottom tangle is a tangle in a cube consisting of arc components whose boundary points are on a line in the bottom square of the cube. A ribbon bottom tangle is a bottom tangle whose closure is a ribbon link. For every $n$-component ribbon bottom tangle $T$, we prove that the universal invariant of $T$ associated to the quantized enveloping algebra $U_h(sl_2)$ is contained in a certain subalgebra of the $n$-fold completed tensor power of $U_h(sl_2)$. This result is applied to the colored Jones polynomial of ribbon links. |
| 日時 | 2009年7月17日（金）16：00～17：00 |
| 講演者（所属） | 張 娟姫（広島大学） |
| タイトル | Algebraic links with 3-bridge presentations |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | An algebraic link is a link in the three sphere whose double branched covering is a graph manifold. In this talk, we give a classification of 3-bridge algebraic links and their 3-bridge presentations up to isotopy. We use genus-2 Heegaard splittings of graph manifolds to classify them. In particular, we focus on the relation between 3-bridge presentations for links and genus-2 Heegaard splittings of 3-manifolds, and show with an example how to distinguish two 3-bridge spheres up to isotopy. |
| 日時 | 2009年7月3日（金）16：00～17：00 |
| 講演者（所属） | 丹下 基生（京都大学数理解析研究所） |
| タイトル | Branched covering description of lens space surgery |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | The speaker has studied knots in Poincare homology sphere yielding lens spaces by Dehn surgery. From the fact that the examples are strongly invertible, we concretely describe the Dehn surgeries. As a corollary we show that a class of Brieskorn homology spheres and the splicing of them give rise to lens spaces by Dehn surgery. |
| 日時 | 2009年6月26日（金）16：10～17：10 |
| 講演者（所属） | 矢口 義朗（広島大学） |
| タイトル | Determining the Hurwitz orbit of any tuple of the standard generators of the braid group |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | Hurwitz action of the $n$-braid group $B_n$ on the $n$-fold direct product ${B_m}^n$ of the $m$-braid group $B_m$ is studied. We determine the orbit of any $n$-tuple of the $n$ distinct standard generators of $B_{n+1}$. In addition, we show that any $n$-tuple of the $n$ distinct standard generators of $B_{n+1}$ is transformed into any of those by Hurwitz action together with the action of $B_{n+1}$ by conjugation. |
| 日時 | 2009年6月26日（金）15：00～16：00 |
| 講演者（所属） | 屋代 司（Sultan Qaboos University） |
| タイトル | On annulus twist tracks |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | A generic surface in $3$-space can be deformed into another generic surface by a finite sequence of local moves. Some of these sequence can be viewed as projected images of isotopy deformations of a surface embedded in $4$-space. We call such a sequence liftable. In this talk we will discuss about special regular homotopy deformations on an annulus called annulus twist track. We give a necessary and sufficient condition for an annulus twist track to be liftable. |
| 日時 | 2009年6月19日（金）16：00～17：00 |
| 講演者（所属） | 新國 亮（東京女子大学） |
| タイトル | A refinement of Conway-Gordon's theorem |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | In 1983, Conway and Gordon showed that for every spatial complete graph on 6 vertices, the sum of linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum of Arf invariants over all of Hamiltonian knots is also congruent to 1 modulo 2. In this talk, we give an integral lift of Conway-Gordon's theorem and its applications. |
| 日時 | 2009年6月12日（金）16：00～17：00 |
| 講演者（所属） | 栗屋 隆仁（京都大学数理解析研究所） |
| タイトル | Tame knot theory and knot mosaic theory are equivalent |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | J. Lomonaco Jr and Louis H. Kauffman conjectured that tame knot theory and knot mosaic theory are equivalent. We give a proof of the Lomonaco-Kauffman conjecture. |
| 日時 | 2009年6月5日（金）16：10～17：10 |
| 講演者（所属） | Iain Aitchison（University of Melbourne） |
| タイトル | Explicit moduli for closed genus 2 surfaces (joint work with Armando Rodado) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | We explicitly describe the Teichmuller and Moduli spaces for closed surfaces
of genus 2, following the path suggested by Rivin, Leibon and Springborn:
(Compactified) Teichmuller space is tiled by copies of 10 explicit 6-dimensional
polyhedra, each parametrizing the possible realizations in hyperbolic geometry
of a Delauney triangulation/circle pattern with one of 10 specified underlying
graphs. Coordinates for the polyhedra allow the surface to be explicitly reconstructed as a hyperbolic surface. Symmetries of the polyhedra can be explicitly described, thereby giving the corresponding decomposition of moduli space. This answers, in the genus 2 case, questions raised by Sullivan and Witten in recent years: that Weierstrass points may help to describe moduli for closed surfaces, and that there may be a cell decomposition with natural compactification for closed surfaces of genus 2 or more. This is the first explicit cell decomposition of the (compactified) moduli space of any closed hyperbolic surface. The approach uses the fixed points of the unique hyperelliptic involution on genus 2 surfaces, which is an isometry with respect to any hyperbolic structure, and had been suggested by Aitchison at Xi'an in 2002. Rodado completed his PhD at Melbourne, implementing this approach using linear programming underlying circle patterns, and finding all candidate graphs describing generic Delaunay circle patterns. We thus describe Rodado's work, and subsequent joint work explicitly describing the 10 6-dimensional polytopes of the natural compactification of Teichmuller and Moduli space. |
| 日時 | 2009年6月5日（金）15：00～16：00 |
| 講演者（所属） | 野坂 武史（京都大学数理解析研究所） |
| タイトル | Quandles and $C^{\infty}$-manifolds |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | There are many studies for finite quandles. This talk explores manifolds $X$ with a quandle structure and presents some examples and properties of $X$. I show that $X$ is a homogenous space ($X=G/H$) under a natural condition. Moreover, with defining a quandle measure of $X$, I arrive at some results as analogous to cases of finite quandles. |
| 日時 | 2009年5月29日（金）16：10～17：10 |
| 講演者（所属） | 塚本 真輝（京都大学） |
| タイトル | Asymptotic distribution of critical values (joint work with Tomohiro Fukaya) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | Let $X$ be a closed manifold and $f:X\times X\to \mathbb{R}$ be a smooth
function. Define $f_n:X^{n+1}\to \mathbb{R}$ by $f_n(x_1, \cdots, x_{n+1}) := \sum f(x_i, x_{i+1})/n$. We study the asymptotic distribution of the critical values of $f_n$ as $n$ goes to infinity. This is the joint work with Tomohiro Fukaya. |
| 日時 | 2009年5月29日（金）15：00～16：00 |
| 講演者（所属） | 小畑 久美（OCAMI） |
| タイトル | Knots contained in spatial embeddings of complete graphs and circular embeddings of knots (joint work with Toshifumi Tanaka) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | This is a joint work with Toshifumi Tanaka. We construct a linear spatial embedding of the complete graph on 2n-1 (or 2n) vertices which contains the torus knot of type (2n-5, 2) (n is greater than or equal to 4). And we define the circular number of a knot. We show that a knot has the circular number 3 if and only if the knot is a trefoil knot, and the figure-eight knot has the circular number 4. |
| 日時 | 2009年5月15日（金）16：00～17：00 |
| 講演者（所属） | 岸本 健吾（大阪市立大学） |
| タイトル | The IH-complex of spatial trivalent graphs (joint work with Atsushi Ishii) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | This is a joint work with Atsushi Ishii. An IH-move is a local spatial move of a spatial trivalent graph. We define the IH-distance between two spatial trivalent graphs by the minimal number of IH-moves needed to transform one into the other. We give a lower bound for the IH-distance by using invariants for flowed spatial graphs. We introduce the IH-complex and show some fundamental properties of the complex. |
| 日時 | 2009年5月8日（金）14：00～15：00 |
| 講演者（所属） | 安部 哲哉（大阪市立大学, 日本学術振興会特別研究員（DC2）） |
| タイトル | The band-unknotting number of a knot (joint work with Ryuji Higa) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | This is a joint work with Ryuji Higa. A band-move is a local move of a
link diagram which is performed by adding a band. We define the band-unknotting
number of a knot K to be the minimum number of band-moves needed to transform
a diagram of K into that of the trivial knot. Note that, in the definition
of the band-unknotting number of a knot K, we may use Reidemeister moves
after applying a band-move and the sequence from a diagram of K to that
of the trivial knot may contain a diagram of a link. In this talk, we show that the band-unknotting number of a knot K is less than or equal to half the crossing number of K and the equality holds if and only if K is the trivial knot or the figure-eight knot. To prove this, we give a characterization of the figure-eight knot. |
| 日時 | 2009年4月24日（金）14：00～15：00 |
| 講演者（所属） | Daniel Moskovich（京都大学数理解析研究所） |
| タイトル | Equivalence relations generated by surgeries which preserve metabelian information |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | We consider knots modulo surgery which preserved metabelian subgroups of the knot group. When these subgroups are fixed and finite, the number of equivalence classes is finite. For certain groups the equivalence classes can be completely determined. Universally, the maximal metabelian subgroup of a knot is preserved by surgeries along unit-framed links which form boundary links with the knot. The induced equivalence relation interpolates between loop Y_1-equivalence (S-equivalence) and loop Y_2-equivalence. |
| 日時 | 2009年4月17日（金）16：00～17：00 |
| 講演者（所属） | 鄭 仁大（大阪市立大学） |
| タイトル | On a simplicial complex of the Alexander polynomials |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | We detect whether a reciprocal integer polynomial $f(t)=\sum_{i=1}4 a_i
t^i$ with $|a_0| \le 100$ is realized as the Alexander polynomial of an
alternating knot. In addition, we introduce a simplicial complex structure on the set of the Alexander polynomials and study a subcomplex consists of the Alexander polynomials of alternating knots. |
| 日時 | 2009年4月10日（金）16：00～17：00 |
| 講演者（所属） | 塚本 達也（大阪工業大学） |
| タイトル | Delta-cobordism of certain satellite links (joint work with Tetsuo Shibuya and Akira Yasuhara) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | This is a joint work with Tetsuo Shibuya and Akira Yasuhara. Delta-cobordism is the equivalence relation generated by cobordism and self delta-moves. We study a relation between delta-cobordism of certain satellite links and delta-cobordism of their cores. |
