| Date |
December 11 (Fri.) 16：00～17：00 |
| Speaker |
Kazuto Takao (Institute of Mathematics for Industry, Kyushu University) |
| Title |
On bridge positions, bridge decompositions and bridge spheres |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
The concept of "bridge" is widely known to knot theorists, but in some different ways.
The difference turns out substantial when they discuss isotopies of it.
In this talk, I will compare the notions of bridge position, bridge decomposition and bridge sphere,
and survey the structures formed by the isotopy classes of them.
This is partially joint work with Y. Jang, T. Kobayashi and M. Ozawa. |
| Date |
December 4 (Fri.) 16：00～17：00 |
| Speaker |
Atsuhide Mori (OCAMI) |
| Title |
Transverse knots in confoliation theory |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Confoliation is an intermediary notion between contact structure and foliation.
One of the main theme of confoliation theory is to deform a contact structure to a folaition.
We can deform a given contact structure $D$
on a closed 3-manifold into (the tangent bundle of) a foliation $F$
through a family of contact structures.
Consider a transverse knot $K$ of $D$
and deform it through a family of transverse knots
into a transverse knot of $F$.
Of course, in general, there is no such deformations.
In the happy case where any transverse knot of $D$
can be deformed into that of $F$, we say that
the convergence of $D$ into $F$ is good.
As for a good convergence, $D$ is tight if and only if
$F$ satisfies the relative Thurston inequality.
We sketch the proof of good convergence in a certain case.
This talk is partially based on a collaboration with Yoshihiko Mitsumatsu. |
| Date |
November 13 (Fri.) 16：00～17：00 |
| Speaker |
Jieon Kim（Osaka City University, JSPS） |
| Title |
(Bi)quandle cocycle invariants for links and surface-links |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A quandle is a set equipped with a binary operation satisfying certain axioms derived from Reidemeister moves.
J.S. Carter, D. Jelsovsky, S. Kamada, L. Langford and M. Saito introduced quandle cohomology theory and quandle cocycle invariants for oriented links and surface-links.
J.S. Carter, S. Kamada and M. Saito defined shadow quandle cocycle invariants for oriented links and surface-links, and S. Kamada and K. Oshiro defined symmetric quandle cocycle invariants for unoriented surface-links using symmetric quandle homology theory.
These quandle cocycle invariants for surface-links are defined by using broken surface diagrams.
In this talk, I'd like to describe these quandle cocycle invariants via marked graph diagrams and introduce shadow biquandle cocycle invariants for oriented surface-links.
This is a joint work with S. Kamada and S.Y. Lee. |
| Date |
November 6 (Fri.) 16：00～17：00 |
| Speaker |
Maria de los Angeles Guevara Hernandez（OCAMI） |
| Title |
Families of non-alternating knots |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
First, we will give formulas to calculate the Homfly polynomial of knots formed by 3-tangles.
After that, we will construct families of non-alternating knots and give explicit formulas to calculate the Alexander polynomial of them.
The knots in these families are prime and of alternation number one. Furthermore, they are hyperbolic except for the only two torus knots.
The families contain the first non-alternating knots: $8_{19}$, $8_{20}$, $8_{21}$. |
| Date |
October 30 (Fri.) 16：00～17：00 |
| Speaker |
Yoshiyuki Yokota (Tokyo Metropolitan University) |
| Title |
A topological invariant of graphs in 3-space and its application |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
In this talk, we review the construction of a polynomial invariant of graphs in 3-space.
As an application,
we give some estimates for the tunnel number and the generalized bridge number of bouquets. |
| Date |
October 16 (Fri.) 16：00～17：00 |
| Speaker |
Shin Satoh (Kobe University) |
| Title |
Noded knots and ribbon Kb-knots |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A knotted torus or Klein bottle in Euclidian $4$-space is called a
$T^2$-knot or Kb-knot, respectively. It is known that any ribbon
$T^2$-knot is presented by a welded knot. In this talk, we will
introduce the notion of noded knots and prove that any ribbon Kb-knot is
presented by some noded knot. We also study several properties of a
noded knot presentation. In particular, we discuss a Kb-knot presented
by a noded knot obtained from a classical knot by replacing a classical
crossing with a welded one. |
| Date |
October 9 (Fri.) 16：30～17：30 |
| Speaker |
Kengo Kawamura (Osaka City University) |
| Title |
Surface-knots with self-intersections in the 4-space |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Ribbon singularity and clasp singularity are typical types of singularities appearing in immersions of surfaces into the 3-space.
A knot is called ribbon if it appears as the boundary of an immersed 2-disk with ribbon singularities.
A 2-knot or a surface-knot is called ribbon if it bounds an immersed 3-disk or handlebody with ribbon singularities.
In this talk,
we introduce the notion of a ribbon-clasp surface-knot,
which appears as the boundary of an immersed 3-disk or handlebody with ribbon singularities and clasp singularites. |
| Date |
July 24 (Fri.) 16：00～17：00 |
| Speaker |
Kazuhiro Ichihara (Nihon University) |
| Title |
On the most expected number of components for random links |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We consider a random link, which is defined as the closure of a braid
obtained from a random walk on the braid group. For such a random link,
the expected value for the number of components was calculated by Jiming
Ma.
In this talk, we determine the most expected number of components
for a random link, and further, consider the most expected partition of
the number of strings for a random braid.
This is based on joint work with Ken-ichi Yoshida (Nihon University). |
| Date |
July 17 (Fri.) 16：00～17：00 |
| Speaker |
Hironobu Naoe (Tohoku University) |
| Title |
Corks with shadow complexity one |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Cork is a compact Stein surface which gives rise to exotic pairs of 4-manifolds.
We find infinitely many corks with shadow complexity one among the 4-manifolds constructed from contractible special polyhedra having one true vertex by using the notion of Turaev's shadow.
We also show that there are just two types of polyhedra which are shadows of corks with shadow complexity one. |
| Date |
July 10 (Fri.) 16：00～17：00 |
| Speaker |
Hidetoshi Masai (The University of Tokyo, JSPS) |
| Title |
Fibered commensurability of random mapping classes |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We consider random walk on the mapping class group to generate
"random" mapping classes. In the first half of this talk I will
summarize basic properties and important known facts about random walk
on the mapping class group. Then I will introduce the notion called
fibered commensurability and discuss it for random mapping classes. |
| Date |
July 3 (Fri.) 16：00～17：00 |
| Speaker |
Takahiro Oba (Tokyo Institute of Technology) |
| Title |
Compact Stein surfaces and braided surfaces |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Loi and Piergallini showed that any compact Stein surface is the total space
of a simple branched covering of a 4-ball whose branch set is a positive braided
surface. They also showed that the opposite is true. Unfortunately, although the
fact is well-known, little is known about how Stein structures behave towards
positive braided surfaces. In this talk, we give an infinite family of positive
braided surfaces as branch sets of simple branched coverings whose total spaces
are all diffeomorphic but admit mutually different Stein structures. |
| Date |
June 26 (Fri.) 16：00～17：00 |
| Speaker |
Kouichi Yasui (Hiroshima University) |
| Title |
Corks, exotic 4-manifolds and knot concordance |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We give a method for producing framed knots which represent homeomorphic
but non-diffeomorphic (Stein) 4-manifolds, using corks and satellite maps.
To obtain the method, we introduce a new description of cork twists. As
an application, we construct knots with the same 0-surgery which are not
concordant for any orientations. This disproves the Akbulut-Kirby conjecture
given in 1978. |
| Date |
June 19 (Fri.) 16：00～17：00 |
| Speaker |
Masahiko Saito (University of South Florida) |
| Title |
Homology for quandles with partial group operations |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
This is a joint research with Scott Carter, Atsushi Ishii and Kokoro Tanaka.
A quandle is a set that has a binary operation satisfying three conditions
corresponding to the Reidemeister moves.
A quandle that is a union of groups with the operation restricting to conjugation on each group component
is called a multiple conjugation quandle.
In this definition,
compatibilities between the group and quandle operations are imposed which are motivated by considerations on colorings of handlebody-links.
In this talk,
a homology theory for multiple conjugation quandles is presented that unifies group and quandle homology theories.
Algebraic aspects, such as extensions, are discussed,
and degenerate subcomplexes are defined
in relation to simplicial decompositions of prismatic (products of simplices) complexes.
Cocycle invariants are defined for handlebody-links using this homology theory. |
| Date |
June 12 (Fri.) 16：00～17：00 |
| Speaker |
Tetsuya Ito (RIMS) |
| Title |
Homological representation prospect of quantum $sl_2$ invariants |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We explain a description of quantum $sl_2$ invariants (loop
expansion, colored Alexander invariant) of knots in terms of homological
braid group representations,
which helps us to understand topological
content of quantum $sl_2$ invariants. |
| Date |
June 5 (Fri.) 16：00～17：00 |
| Speaker |
Motoo Tange (University of Tsukuba) |
| Title |
Heegaard Floer homology of Matsumoto's manifolds |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Let $X_n$ be a 4-manifold obtained by attaching two
trefoils with linking number $1$ and with the framings $(0,n)$. Y.
Matsumoto asked in the Kirby's problems list whether two generators in
$H_2(X_0)$ can be realized by the embedded edge of two spheres. We
discuss when the boundary $M_n$ of $X_n$ bounds a contractible
4-manifold by using Heegaard Floer homology. $M_n$ is 1-surgery of the
n-twisted Whitehead double $K_n$ of the trefoil, and we will determine
the 4-ball genus of $K_n$ by using the obstruction by Owens and Strle. |
| Date |
May 29 (Fri.) 16：00～17：00 |
| Speaker |
Yasutaka Nakanishi (Kobe University) |
| Title |
From a surgical view of Alexander invariants |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
The Alexander polynomial is an effective knot invariant
untill now. Levine and Rolfsen introdoced a surgical view of Alexander
invariants. In this talk, the speaker will talk on the surgical view and
its applications: unknotting number and knot adjacency. |
| Date |
May 15 (Fri.) 16：00～17：00 |
| Speaker |
Patrick Dehornoy（University of Caen, France） |
| Title |
The alternating normal form of braids |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Beside Artin's standard "combing normal form" and
Garside-Adjan-Morton-Thurston equally well-known "greedy normal form",
we develop another natural and simple normal form of braids based on the
embedding of (n-1)-strand braids into n-strand braids. This approach is
specially well adapted for analyzing the canonical ordering of positive
braids and it leads to paradoxically long sequences and, from there
(joint work with L.Carlucci and A.Weiermann), to unprovability
statements for certain games involving braids. |
| Date |
May 8 (Fri.) 16：00～17：00 |
| Speaker |
Kuniyuki Takaoka (Waseda University) |
| Title |
On left-right words and positive-negative words obtained from knot diagrams |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
In knot theory, knot diagrams play an important role to study and classify
knots. For the crossing points of an oriented knot diagram, we have three
points of view: over/under crossing, left/right crossing and positive/negative
crossing. In 2012, Higa, Nakanishi, Satoh and Yamamoto defined an OU sequence
for a knot diagram, where the OU sequence is obtained from crossing information
by reading a sequence of over/under crossing points along the orientation
direction of a knot. They mainly studied sequences which are realized by
diagrams of the trefoil knot. In this talk, we will focus on left/right
crossing and positive/negative crossing for a knot diagram and study the
cyclic words obtained from the crossing sign. In the case of focusing on
left/right crossing information, this information does not reflect any
over/under crossing information. Therefore we treat a spherical closed
curve instead of a knot diagram. |
| Date |
May 1 (Fri.) 16：00～17：00 |
| Speaker |
Ryo Nikkuni (Tokyo Woman's Christian University) |
| Title |
On calculations of the twisted Alexander ideals for spatial
graphs,
handlebody-knots and surface-links |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We calculate the twisted Alexander ideals for spatial
graphs, handlebody-knots, and surface-links. For spatial graphs, we
calculate the invariants of Suzuki's theta-curves and show that the
invariants are nontrivial for Suzuki's theta-curves whose Alexander
ideals are trivial. For handlebody-knots, we give a remark on
abelianizations and calculate the invariant of the handlebody-knots up
to six crossings. For surface-links, we correct Yoshikawa's table and
calculate the invariants of the surface-links in the table. This is a
joint work with Atsushi Ishii (University of Tsukuba) and Kanako Oshiro
(Sophia University). |
| Date |
April 24 (Fri.) 16：00～17：00 |
| Speaker |
Shosaku Matsuzaki (Waseda University) |
| Title |
Arrangements of links on surfaces arranged in $\mathbb{R}^3$ |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A finite set of two-dimensional manifolds embedded in
three-dimensional Euclidean space is called an $\textit{arrangement}$
$\textit{of}$ $\textit{surfaces}$. A link $L$ is said to be
$\textit{arrangeable}$ on an arrangement
$\mathcal{F}$ of surfaces if there exists a link $L'$ which is ambient
isotopic to $L$ such that each component of $L'$ is contained in a
surface belonging to $\mathcal{F}$. We consider the following problems.
(1) Given an arrangement of surfaces, determine links which can be
arrangeable on it. (2) Given a link, determine arrangements of surfaces
on which the link is arrangeable. I will talk about partial answers to
the problems. |
| Date |
April 17 (Fri.) 16：00～17：00 |
| Speaker |
Hideo Takioka (OCAMI) |
| Title |
A characterization of the $\Gamma$-polynomials of knots
with the clasp numbers at most two |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
It is known that every knot bounds a singular disk whose
singular set consists of only clasp singularities. Such a singular disk
is called a clasp disk. The clasp number of a knot is the minimum number
of clasp singularities among all clasp disks of the knot. The
$\Gamma$-polynomial is the common zeroth coefficient polynomial of both
the HOMFLYPT and Kauffman polynomials. I will talk about a
characterization of the $\Gamma$-polynomials of knots with the clasp
numbers at most two. |
| Date |
April 10 (Fri.) 16：30～17：30 |
| Speaker |
Tetsuya Abe (OCAMI) |
| Title |
Infinitely many ribbon disks with the same exterior |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A classical Gluck's theorem states that there exist at most two inequivalent
2-knots with diffemorphic exteriors. In this talk, we construct infinitely
many ribbon disks with the same exterior. First, we give a sufficient condition
for a given slice disk to be ribbon. Next, we construct infinitely many
slice disks with the same exterior, and prove that these are ribbon. This
is a joint work with Motoo Tange. If time permits, we prove that these
ribbon disks are mutually distinct by the (overtwisted) contact structures
in the 3-sphere. |
Last Modified on May 14, 2015
