| Speaker |
Motoo Tange (University of Tsukuba) |
| Title |
Ribbon disk in 4-dimensional handle diagram |
| Date |
December 21 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A ribbon disk in S^3 means an immersion of disk that the set of singularities of the disk is interval-type double points and satisfies ribbon condition.
We call the handle diagram containing a holed ribbon disk a PR-diagram (perforated ribbon diagram) and the ribbon disk a PR-disk.
We explain several PR-disk diagram moves for a PR-diagram. As an application of the moves,
we prove any slice knot is the boundary of a regular PR-disk in a handle diagram consisting of modified canceling pairs. |
| Speaker |
Yoshikazu Yamaguchi (Akita University) |
| Title |
Twisted Alexander invariants and metabelian representations |
| Date |
December 14 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
It has been revealed that we need non-abelian representations of knot groups to obtain nice applications by the twisted Alexander invariants.
Finding representations is sometimes a difficult aspect of computing the twisted Alexander invariants.
There exist several constructions to make reasonable non-abelian representations which are called metabelian.
In this talk, we explain the constructions and properties of metabelian representations and discuss some applications of the twisted Alexander invariants for metabelian representations. |
| Speaker |
Shin Satoh (Kobe University) |
| Title |
No 2-knot has regular triple point number four |
| Date |
November 30 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We explain how to get the double decker set of a surface-knot diagram from the double point set by using a Gauss diagram with trivalent chords.
As an application, we give several properties of double point set of a regular 2-knot diagram, and prove that there is no 2-knot whose regular triple point number is equal to four. |
| Speaker |
Byeorhi Kim (Kyungpook National University) |
| Title |
A study of quandle extensions by cocycles |
| Date |
November 9 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
In 2003, quandle extensions by cocycles were first introduced by N, Andruskiewitsch, M. Grana and J. S. Carter, M. Elhamdadi, M.A. Nikiforou, M. Saito, respectively.
In 2017, I introduced some sufficient conditions for an operation table to be a quandle, when the operation table is decomposable as sub-tables.
In fact, a quandle extension by the trivial cocycle is one of typical examples with decomposable operation table.
Recently, J. S. Carter and I are studying mod-2 extensions of some quandles by using their inner automorphism groups.
In this talk, I will introduce these two studies of quandle extensions and observe relation between quandle extensions and group extensions. |
| Speaker |
Naoki Sakata (Saitama University, Graduate School of Science and Engineering) |
| Title |
Veering triangulations of some hyperbolic fibered arborescent link complements |
| Date |
November 2 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Agol proved that every pseudo-Anosov mapping torus of a surface, punctured along the singular points of the stable and unstable foliations, admits a canonical “veering” ideal triangulation.
In this talk, we describe the veering triangulations of the complements of some hyperbolic fibered arborescent links.
We also give an upper bound for the hyperbolic volume of such an arborescent link complement. The upper bound depends on the number of “hinge” tetrahedra in the veering triangulation. |
| Speaker |
Shin'ya Okazaki（OCAMI） |
| Title |
Litherland's Alexander polynomial for handlebody-knots |
| Date |
October 26 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Litherland introduced another version of the Alexander polynomial for theta-curves.
Litherland's Alexander polynomial of a theta-curve includes information of the constituent knots of the theta-curve.
In this talk, we extend Litherland's Alexander polynomial of a theta-curve to that of a handlebody-knot. We consider the constituent knots of a handlebody-knot by Litherland's Alexander polynomial. |
| Speaker |
Hideo Takioka（OCAMI） |
| Title |
4-move distance of knots |
| Date |
October 19 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
4-move is a local change for knots and links which changes 4 half twists to 0 half twists or vice versa. In 1979, Yasutaka Nakanishi conjectured that every knot can be changed by 4-moves to the trivial knot.
This is still an open problem. In this talk, we consider 4-move distance of knots, which is the minimal number of 4-moves needed to deform one into the other.
In particular, the 4-move unknotting number of a knot is the 4-move distance to the trivial knot. We give a table of the 4-move unknotting number of knots with up to 9 crossings.
This is a joint work with Taizo Kanenobu. |
| Speaker |
Toshio Saito (Joetsu University of Education) |
| Title |
Tunnel number of knots and generalized tangles |
| Date |
July 13 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
It is known that there is a fundamental inequality related to tunnel number of a knot and tangles
obtained by its tangle decomposition. The inequality gives an upper bound for tunnel number of the knot, and there exists a knot in the 3-sphere so that the inequality is non-strict.
This talk will discuss a slight generalization of those. |
| Speaker |
Katsumi Ishikawa (Research Institute for Mathematical Sciences, Kyoto University) |
| Title |
A link-homotopy invariant for surface links |
| Date |
June 29 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A surface link is an oriented closed (not necessarily connected) surface smoothly embedded in the 4-sphere. Any 2-link, i.e. a surface link with all components being 2-spheres,
is known to admit a link homotopy which pulls the 2-spheres apart, but we know only a little about homotopy classification of other surface links: for example, we have only a few link-homotopy invariants for them.
In this talk, we introduce a link-homotopy invariant for surface links as a refinement of the asymmetric linking number. This is a surface-link version of Milnor's link-homotopy invariant for 1-links,
and the triple linking number is also calculated from it. |
| Speaker |
Wataru Yuasa (Kyoto University) |
| Title |
$A_2$ colored polynomials of rigid vertex graphs |
| Date |
June 22 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A one-variable specialization of the Kauffman-Vogel polynomial for an unoriented 4-valent rigid vertex graph was given by using the Kauffman bracket.
In this talk, we will define an $A_2$ version of the one-variable Kauffman-Vogel polynomial for unoriented/oriented 4-valent rigid vertex graphs and show a calculation example. |
| Speaker |
Akio Kawauchi (OCAMI) |
| Date |
June 15 (Fri.) 16：00〜17：00 |
| Title |
|
| Place |
It was canceled due to various reasons. |
| Abstract |
|
| Speaker |
Kodai Wada (Waseda University) |
| Title |
Generalized virtualization on welded links |
| Date |
June 8 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
For each positive integer $n$ we introduce two local moves $V(n)$ and $V^n$, which are generalizations of the virtualization move. We give a classification of welded links up to $V(n)$-move.
In particular, a $V(n)$-move is an unknotting operation on welded knots for any $n$. On the other hand, we give a necessary condition for which two welded links are equivalent up to $V^{n}$-move.
This leads to show that a $V^{n}$-move is not an unknotting operation on welded knots except $n=1$. We also discuss relations among $V^{n}$-moves, associated core groups and the multiplexing of crossings.
This is a joint work with Haruko A. Miyazawa and Akira Yasuhara. |
| Speaker |
Tomo Murao (University of Tsukuba) |
| Title |
Necessary conditions to be constituent handlebody-knots and their application |
| Date |
May 25 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
For a handlebody-knot $H$, a constituent handlebody-knot of $H$ is a handlebody-knot obtained from $H$ by removing an open regular neighborhood of some meridian disks of $H$.
We can deal with the tunnel number and the cutting number uniformly, which are “dual” geometric invariant for handlebody-knots, by introducing the notion of constituent handlebody-knots.
In this talk, we provide necessary conditions to be constituent handlebody-knots by using $G$-family of quandles colorings.
Furthermore we give lower bounds for the tunnel number and the cutting number of handlebody-knots as the corollaries. |
| Speaker |
Erika Kuno (Osaka University) |
| Title |
Abelian subgroups of the mapping class groups for non-orientable surfaces |
| Date |
May 18 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
One of the basic and important problems to study algebraic structures of mapping class groups is finding abelian subgroups included in the mapping class groups.
Birman-Lubotzky-McCarthy in 1983 gave an answer to this question for the orientable surfaces.
In this talk, we give the upper bound of the torsion-free rank of the abelian subgroups for the mapping class groups of non-orientable surfaces. |
| Speaker |
Taizo Kanenobu (Osaka City University) |
| Title |
Classification of ribbon 2-knots by the twisted Alexander polynomials |
| Date |
May 11 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We have classified the oriented ribbon 2-knots presented by virtual arcs with up to four crossings.
In this talk, we consider this classification using the twisted Alexander polynomial associated to SL(2,C)-representation.
We also announce some properties of the twisted Alexander polynomial of a ribbon 2-knot with one fusion. |
| Speaker |
Jung Hoon Lee（Chonbuk National University） |
| Title |
On weak reducing disks and disk surgery |
| Date |
April 27 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Let $K$ be an unknot in $8$-bridge position in the $3$-sphere. We give
an example of a pair of weak reducing disks $D_1$ and $D_2$ for $K$ such
that both disks obtained from $D_i$ ($i = 1, 2$) by a surgery along any
outermost disk in $D_{3-i}$, cut off by an outermost arc of $D_i \cap D_{3-i}$
in $D_{3-i}$, are not weak reducing disks, i.e. the property of weak reducibility
of compressing disks is not preserved by a disk surgery. |
| Speaker |
Sukuse Abe (OCAMI) |
| Title |
Perturbative $\mathfrak{g}$ invariants of genus $2$ handlebody-knots |
| Date |
April 20 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We denote perturbative $\mathfrak{sl}_2$ invariants of genus $2$ handolebody-knots. We try to define a perturbative $\mathfrak{g}$ invariant for the general Lie algebra.
This definition is not yet definitely completed definitions. I want the opinions of many people of mathematician. |
| Speaker |
Kenta Okazaki (RIMS, Kyoto University) |
| Title |
On planar algebras and state sum invariants of 3-manifolds |
| Date |
April 13 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Theory of subfactors has many applications in low dimensional topology, including Jones polynomial of knots, quantum invariants and state sum invariants of $3$-manifolds. Planar algebras, on the other hand, which are defined by using planar operad, enable us to treat extremal subfactors combinatorially. In this talk, we briefly introduce the basic concept of planar algebras, and explain how to construct state sum invariants of $3$-manifolds. In particular, we give an explicit construction of the state sum invariant of $3$-manifolds derived from the subfactor with principal graph $E_8$. |
Last Modified on 2018.12.06
