Schedule of Upcoming Seminar
| Speaker |
Noboru Ito (National Institute of Technology, Ibaraki College) |
| Title |
Splice-unknotting number and crosscap number |
| Date |
January 29 (Fri.) 16：00～17：00 |
| Abstract |
The splice-unknotting number equals the crosscap number for any prime alternating knot (Ito-Takimura 2020, Kindred 2020, independently).
In this talk, the speaker will explain a proof of this result. |
| Speaker |
Motoo Tange (University of Tsukuba) |
| Title |
Distribution of non-zero coefficients for a lens surgery polynomial |
| Date |
January 15 (Fri.) 16：00～17：00 |
| Abstract |
The Alexander polynomial of a lens space knot is called a lens surgery
polynomial. Ozsvath and Szabo proved that such polynomials are flat and
alternating. We investigate the distribution of on-zero coefficients of
a lens surgery polynomial. We prove a new restriction for lens surgery
polynomials by using the connection of the non-zero curve. |
| Speaker |
Ryoma Kobayashi (National Institute of Technology, Ishikawa College) |
| Title |
Infinite presentations for the mapping class group of a compact non orientable surface and its twist subgroup |
| Date |
December 11 (Fri.) 16：00～17：00 |
| Abstract |
The mapping class group of a compact non orientable surface can not be generated by only Dehn twists.
We would like to consider the subgroup of the mapping class group generated by Dehn twists, called the twist subgroup.
In our work, we gave an infinite presentation for this group whose generating set consists of all Dehn twists. On the other hand,
Omori and the speaker already gave an infinite presentation for the mapping class group of a compact non orientable surface. In our work,
we also gave more simple infinite presentations for this group, using the infinite presentation for the twist subgroup. |
| Speaker |
Katsumi Ishikawa (Kyoto University) |
| Title |
Surjective quandle colorings |
| Date |
December 4 (Fri.) 16：00～17：00 |
| Abstract |
Various knot invariants arise from quandles and many of them can be calculated from knot diagrams. However,
it is often overlooked that such invariants include non-effective ones; for example, some 2-cocycle invariants are known to take the trivial value for any coloring.
In this talk, fixing a quandle and a second homology class, we examine when there exists a knot which admits a surjective coloring with the fixed homology class.
In particular, we show that for any finitely generated connected quandle, there exists a knot admitting a surjective coloring. |
| Speaker |
Genki Omori (Tokyo University of Science) |
| Title |
Dehn twist-crosscap slide presentations for involutions on non-orientable surfaces of genera up to 5 |
| Date |
November 27 (Fri.) 16：00～17：00 |
| Abstract |
Lickorish proved that any element of the mapping class group of a non-orientable is a product of Dehn twists and crosscap slides. We call the product a Dehn twist-crosscap slide presentation for the element.
In this talk, we give Dehn twist-crosscap slide presentations for all conjugacy classes of involutions on non-orientable surfaces of genus 4 and 5.
The Dehn twist-crosscap slide presentations are constructed by products of Szepietowski’s finite generating set. This is a joint work with Naoki Sakata (Saitama University). |
| Speaker |
Airi Aso (Tokyo Metropolitan University) |
| Title |
A note on the asymptotic behavior of the twisted Alexander polynomials |
| Date |
November 6 (Fri.) 16：00～17：00 |
| Abstract |
R. M. Kashaev conjectured that the asymptotics of the Kashaev invariant of hyperbolic links gives the hyperbolic volume of the link compliment. H. Murakami and J. Murakami extended Kashaev's conjecture (volume conjecture) and H. Murakami, J. Murakami, M. Okamoto, T. Takata, and Y. Yokota proposed the complexification of the volume conjecture.
On the other hand, H. Goda gave a fomula of hyperbolic volume with twisted Alexander polynomials. Furthermore, J. Park conjectured a relation between the Reidemeister torsion and complex volume.
In this talk, we try to give a complexification of Goda’s formula. To this end, we observe the asymptotics of the twisted Alexander polynomials of some hyperbolic knots. |
| Speaker |
Atsuhiko Mizusawa (Waseda University) |
| Title |
A new presentation of 4-component link-homotopy classes and an algorithm |
| Date |
October 30 (Fri.) 16：00～17：00 |
| Abstract |
Two links (string-links) are link-homotopic if they are transformed to each other by a sequence of ambient isotopies and self-crossing changes.
Habegger and Lin classified the link-homotopy classes of links as the link-homotopy classes of string-links modulo conjugations and partial conjugations.
After that Hughes showed that the partial conjugations generate the conjugations. Habegger and Lin also gave an algorithm which determines whether given two links are link-homotopic or not by using the actions of the partial conjugations.
In this talk, we calculate the actions of the partial conjugations for 4-component string-links through the clasper theory.
This gives a new presentation of the link-homotopy classes of 4-component links and how to run the algorithm.
This also gives an alternative proof of Levine’s classification of the 4-component link-homotopy classes.
This is a joint work with Yuka Kotorii (Hiroshima university / RIKEN). |
| Speaker |
Yuanyuan Bao (The University of Tokyo) |
| Title |
An Alexander polynomial of MOY graphs |
| Date |
October 16 (Fri.) 16：00～17：00 |
| Abstract |
We introduce a polynomial invariant for an MOY graph, which is an oriented graph equipped with a coloring satisfying a certain admissibility condition.
We discuss its relations with Heegaard Floer homology and Viro’s gl(1|1)-Alexander polynomial. Finally, we discuss some properties and applications of this polynomial, such as detection of non-planarity,
relation with weighted number of spanning trees and so on. (A part of the talk is based on joint work with Zhongtao Wu in the Chinese University of HongKong) |
| Speaker |
Tomo Murao (Waseda University) |
| Title |
Multiple group rack colorings for oriented spatial surfaces |
| Date |
October 9 (Fri.) 16：00～17：00 |
| Abstract |
A spatial surface is a compact surface embedded in the 3-sphere. If it has a boundary, the spatial surface is a Seifert surface of the link given by the boundary.
In this talk, we introduce a coloring invariant for oriented spatial surfaces by using a multiple group rack, which is an algebra consisting of a disjoint union of groups equipped with a rack structure.
Then we demonstrate calculations of the invariants of spatial surfaces. This is a joint work with Atsushi Ishii and Shosaku Matsuzaki. |
| Speaker |
Makoto Sakuma (OCAMI, Hiroshima University) |
| Title |
Homotopy motions of surfaces in 3-manifolds |
| Date |
October 2 (Fri.) 16：00～17：00 |
| Abstract |
By relaxing the notion of a motion of a subspace S in a manifold M, we
define a homotopy motion of S in M to be a homotopy F={f_t}: Sx [0,1] ->
M, such that f_0 is the inclusion map j:S->M and f_1 is an embedding
of S with the same image as j. The homotopy motion group P(M,S) is the
group of equivalence classes of motions of S in M, where the product is
defined by concatenation of homotopies. There is a natural homomorphism
from P(M,S) to the mapping class group MCG(S), and we denote its kernel
and image by K(M,S) and G(M,S), respectively. Thus we have the exact sequence
1 -> K(M,S) -> P(M,S) -> G(M,S) -> 1. In this talk we give
a systematic study of these groups for the cases where (i) S is an incompressible
surface in a Haken manifold M, and (ii) S is a Heegaard surface of a closed
orientable 3-manifold M. For the case (i), we give a complete description
of the groups and the exact sequence. For the case (ii), we obtain the
following results. (a) Determination of the group K(M,S) when M is aspherical.
(b) If M has the geometry S^3 or S^2xR, or is a connected sum of S^2xS^1,
then the homological degree gives a nontrivial map from K(M,S) to Z. (c)
If the Heegaard surface S is induced from an open book decomposition of
M and if M is either aspherical or has the nonvanishing Gromov norm, then
G(M,S) is strictly bigger than the natural subgroup associated with S,
which appears in a problem proposed by Minsky concerning the homotopical
behavior of essential simple loops on S in M, and studied by Bowditch-Ohshika-Sakuma
and Fujiwara-Bestvina. In the talk, I will first explain how the concepts
of monodromy groups and homotopy motion groups naturally arise from the
study of Minsky’s question and related questions, and then present basic
ideas of the proofs of the main results. This is a joint work in progress
with Yuya Koda. |
| Speaker |
Kodai Wada (Osaka University) |
| Title |
The Dabkowski-Sahi invariant and 4-moves for links |
| Date |
July 17 (Fri.) 16：00～17：00 |
| Abstract |
Dabkowski and Sahi defined an invariant of a link in the 3-sphere, which is preserved under 4-moves.
This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish the Dabkowski-Sahi invariants of given links.
In this talk, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link.
Using this condition, we provide a practical obstruction to a link to be trivial up to 4-moves. This is a joint work with Haruko A. Miyazawa and Akira Yasuhara. |
| Speaker |
Tatsuro Shimizu (OCAMI) |
| Title |
A geometric description of Riedemeister-Turaev torsion of 3-manifolds |
| Date |
July 3 (Fri.) 16：00～17：00 |
| Abstract |
A representation of the fundamental group of a closed oriented 3-manifold said to be acyclic if the corresponding local system is acyclic.
Reidemeister(-Turaev) torsion can be defined for such an acyclic (and abelian) representation.
In this talk I will give a geometric description of Reidemeister-Torsion by using the two point configuration space of the 3-manifold.
This description is inspired by Chern-Simons perturbation theory. |
| Speaker |
Wataru Yuasa (RIMS, Kyoto University) |
| Title |
Zero stability for the one-row colored sl(3) Jones polynomial |
| Date |
June 26 (Fri.) 16：00～17：00 |
| Abstract |
I will talk on the existence of tails of one-row colored sl(3) colored Jones polynomials for oriented "adequate" links. Armond showed,
conjectured by Dasbach and Lin, that the colored Jones polynomial {J_{n}(L)} of an adequate link L has a stability, called zero stability, of its coefficients.
The zero stability is equivalent to the existence of the tail T(L) which is a q-series such that T(L)=J_{n}(L) mod q^{n+1}Z[q].
I will consider the one-row colored sl(3) Jones polynomial and show its zero stability. |
Last Modified on 2021.1.18
