| Date |
February 21 (Fri.) 16：30～17：15 |
| Speaker |
Gyo Taek Jin（KAIST） |
| Title |
Quadrisecants of unknots |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The conjecture of quadrisecant approximation is true for some minimal polygonal
prime knots. We investigate the conjecture for polygonal unknots. We thank
Ernst Claus for his data of polygonal unknots. |
| Date |
February 21 (Fri.) 15：30～16：15 |
| Speaker |
Hideo Takioka (Osaka City University) |
| Title |
The $\Gamma$-polynomial of a knot and its applications |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The $\Gamma$-polynomial is an invariant of an oriented link in the 3-sphere, which is contained in both the HOMFLYPT and Kauffman polynomials as their common zeroth coefficient polynomial. As applications of the $\Gamma$-polynomial, I will talk about the following three topics:
(1) On the arc index of cable knots (joint with Hwa Jeong Lee, KAIST)
(2) On the braid index of Kanenobu knots
(3) On the arc index of Kanenobu knots (joint with Hwa Jeong Lee, KAIST) |
| Date |
February 21 (Fri.) 14：30～15：15 |
| Speaker |
Hwa Jeong Lee（KAIST） |
| Title |
On the arc index of knots and links |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
Every knot or link $L$ can be embedded in the union of finitely many half
planes which have a common boundary line such that each half plane intersects
$L$ in a single arc. Such an embedding is called an arc presentation of
$L$. The arc index of $L$ is the minimal number of pages among all arc
presentations of $L$. It is known that the arc index of a knot is closely
related to the minimal crossing number of the knot. In this talk, we present
a small survey on arc index and compute the arc index of some of Pretzel
knots and Montesinos links. |
| Date |
February 21 (Fri.) 13：30～14：15 |
| Speaker |
Shin'ya Okazaki (OCAMI) |
| Title |
Seifert manifolds and $0$-surgery |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
For closed connected orientable $3$-manifold $M$, let $c(M)$ be the minimal
number of the component number of any link $L$ whose each component is
the unknot in $S^3$ such that $M$ is obtained by the $0$-surgery of $S^3$
along $L$. Then $c(M)$ is an invariant of closed connected orientable $3$-manifold
$M$. We have already obtained $c(M)$ for some lens spaces. In this talk,
we consider some Seifert manifolds obtained by the $0$-surgery of $S^3$
along a pure $3$-braid link, and we determine $c(M)$ for some Seifert manifolds.
Moreover, we calculate the bridge genus and the braid genus for some Seifert
manifolds. |
| Date |
January 17 (Fri.) 16：00～17：00 |
| Speaker |
Taizo Kanenobu (Osaka City University) |
| Title |
H(2)-Move and Other Local Moves on Knots |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
An H(2)-move is a local move on an unoriented knot which is realized by
smoothing a crossing. This is an unknotting operation, that is, any knot
can be unknotted by a sequence of H(2)-moves. So, we may define an H(2)-unknotting
number and H(2)-Gordian distance. We introduce several methods to give
a lower bound of the H(2)-Gordian distance, which allow us to improve the
table of H(2)-Gordian distances for knots with up to seven crossings. We
also consider a relation with the band surgery and delta move. |
| Date |
January 10 (Fri.) 16：00～17：00 |
| Speaker |
Ayumu Inoue (Aichi University of Education) |
| Title |
Colorings of torus knots and PL trochoids |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The set consisting of rotations of the Euclidean plane is obviously equipped
with the structure of a quandle. In this talk, we show that we have a non-trivial
coloring of a torus knot by the quandle related to a PL trochoid. |
| Date |
December 13 (Fri.) 16：00～17：00 |
| Speaker |
Yeonhee Jang (Nara Women's University) |
| Title |
Bridge splittings of links with Hempel distance $n$
diagrams of types A and D |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
Hempel distance of bridge splittings of links is a measurement of certain
complexity of bridge splittings. The distance is known to reflect some
topological and geometric properties of bridge splittings and links themselves.
In this talk, we show the existence of bridge splittings of links with
Hempel distance exactly $n$ for any given integer $n$. This is a joint
work with Ayako Ido and Tsuyoshi Kobayashi. |
| Date |
November 29 (Fri.) 16：00～17：00 |
| Speaker |
Kanako Oshiro (Sophia University) |
| Title |
Linear Alexander quandle colorings and finite-fold cyclic
covers of $S^3$ branched over knots |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The Fox-colorings of a knot are interpreted as the group representations
from the fundamental groups of the $2$-fold cyclic cover of $S^3$ branched
over the knot to $\mathbb Z_p$. The interpretation is extended for linear
Alxander quandle colorings by using some condition. |
| Date |
November 29 (Fri.) 15：00～16：00 |
| Speaker |
Philippe Humbert（University of Strasbourg） |
| Title |
Higher genus tangles |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
This talk will be about tangles (knots, braids...) lying in a cylinder
over a closed surface of arbitrary genus. I will first introduce some kind
of planar diagrams and Reidemeister-like moves for these objects. This
diagrammatic point of view will then lead to a universal property stated
in the language of braided categories. |
| Date |
November 22 (Fri.) 16：00～17：00 |
| Speaker |
Akira Yasuhara (Tokyo Gakugei University) |
| Title |
$C_k$-concordance group of $n$-string links
(joint work with Jean-Baptiste Meilhan (University of Grenoble I)) |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The $C_k$-equivalence is an equivalence relation on $n$-string links which
is genarated by $C_k$-move and concordance. The set of $C_k$-concordance
classes of $n$-string links has a group structure. We decide when the quotient
groups become abelian. In particular, we show that the $C_9$-concordance
group of 2-string links is not abelian. |
| Date |
November 22 (Fri.) 15：00～16：00 |
| Speaker |
Kokoro Tanaka (Tokyo Gakugei University) |
| Title |
Regular-equivalence of 2-knot diagrams and sphere eversions |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
A surface-knot diagram is said to be regular if it has no branch points.
In this talk, we construct two regular diagrams of a $2$-knot such that
any sequence of Roseman moves between them involves branch points. This
is a joint work with Masamichi Takase (Seikei University). |
| Date |
November 8 (Fri.) 16：00～17：00 |
| Speaker |
Mikami Hirasawa (Nagoya Institute of Technology) |
| Title |
A generalization of the Murasugi sum of Seifert surfaces |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The Murasugi sum is a natural operation to glue two Seifert surfaces. Let
F = G ＊ H be a Murasugi sum of two Seifert surfaces G and H. Then the following
are well-known:
(i) F is of minimal genus if and only if so are G and H.
(ii) F is a fiber surface if and only if so are G and H.
In this talk, we generalize the notion of Murasugi sum by using surfaces
other than a disk, and show that the operation also enjoys the above-mentioned
properties.
Neumann & Rudolph have introduced the notion of "unfoldings"
in n-dimensional knot theory. However, in case n=3, all known examples
of unfoldings are realized as decompositions of Murasugi sums. We give
examples of our operation which are not Murasugi sums or "unfoldings".
After formulating the gap between out operation and the Murasugi sum, we
show that the gap can be arbitrarily large. |
| Date |
November 1 (Fri.) 16：00～17：00 |
| Speaker |
Yuka Kotorii (Tokyo Institute of Technology) |
| Title |
The relation between Milnor mu-invariant and HOMFLYPT
polynomial for links |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
This is joint work with Akira Yasuhara (Tokyo Gakugei University).
For an ordered, oriented link in the 3-sphere, J. Milnor defined a family
of invariants, known as Milnor $\overline{\mu}$-invariants. For an $n$-component
link, Milnor invariant is specified by a sequence of elements of $\{1,
2, \ldots, n \}$ and the length of the sequence is called the length of
the Milnor invariant. J.-B. Meilhan and A. Yasuhara showed that any Milnor
$\overline{\mu}$-invariant of length between 3 and $2k+1$ can be represented
as a combination of HOMFLYPT polynomial of knots obtained by certain band
sum of the link components, if all $\overline{\mu}$-invariants of length
$\leq k$ vanish. In this talk, we improve their formula to give the $\overline{\mu}$-invariants
of length $2k+2$ by adding correction terms. The correction terms can be
given by a combination of HOMFLYPT polynomial of knots determined by $\overline{\mu}$-invariants
of length $k+1$. In particular, for any 4-component link the $\overline{\mu}$-invariants
of length 4 are given by our formula, since all $\overline{\mu}$-invariants
of length 1 vanish. |
| Date |
October 18 (Fri.) 16：00～17：00 |
| Speaker |
Yoshiro Yaguchi (Gunma National College of Technology) |
| Title |
Cords on a 3-times punctured disk |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
A cord is a simple curve on a punctured disk, which connects two punctures.
In this talk, we introduce diagrams which represent isotopy classes of
cords. Using such diagrams, we make up a list of all isotopy classes of
cords on a 3-times punctured disk. As a result, it is shown that they are
completely parameterized by 3 non-negative integers. |
| Date |
October 11 (Fri.) 16：00～17：00 |
| Speaker |
Tetsuya Abe (Tokyo Institute of Technology, JSPS Research Fellow PD) |
| Title |
Infinitely many ribbon disks with the same exterior |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
In 1962, Gluck proved that there are, at most, two different 2-knots with
the same exterior. In 1976, Gordon proved that there exist two different
2-knots with the same exterior.
In this talk, we consider an analogues problem for ribbon disks in the
4-ball D^4. We observe that there exist infinitely many ribbon disks with
the same exterior. This result follows from the previous joint work with
M.Tange. We also study whether the exterior is a handlebody bundle over
S^1. |
| Date |
October 4 (Fri.) 16：00～17：00 |
| Speaker |
Noboru Ito (Waseda Institute for Advanced Study) |
| Title |
(1, 2), weak (1, 3), and strong (1, 3) homotopies on knot
projections |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The speaker plans to talk about a joint work with Yusuke Takimura (Waseda
University, School of Education, M2). First, we obtain the necessary and
sufficient condition that when two knot projections are related by a finite
sequence of the first and second flat Reidemeister moves. Second, we introduce
weak (1, 3) homotopy that is an equivalence relation on knot projections,
defined by the first flat Reidemeister move and one of the third flat Reidemeister
moves. Third, using a map sending weak (1, 3) homotopy classes to knot
isotopy classes, we determine which knot projections are trivialized under
weak (1, 3) homotopy.
If time permits, the speaker will discuss another joint work with Y. Takimura
and K. Taniyama. The joint work introduces strong (1, 3) homotopy that
is an equivalence relation on knot projection, defined by the first flat
Reidemeister move and another type of the third flat Reidemeister moves.
Showing that Hanaki's trivializing number is weak (1, 3) invariant and
introducing cross chord numbers that produce a strong (1, 3) invariant,
we claim that two knot projections having trivializing number two are weak
(1, 3) homotopy equivalent and strong (1, 3) homotopy equivalent if and
only if the two knot projections with trivializing number two can be related
by only the first flat Reidemeister moves. We also determine the strong
(1, 3) equivalence class containing the trivial knot projection and other
classes of knot projections. |
| Date |
July 19 (Fri.) 16：00～17：00 |
| Speaker |
Inasa Nakamura (Gakushuin University) |
| Title |
Triple point cancelling numbers of torus-covering knots |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
It is known that any surface knot can be transformed to an unknotted surface
knot or a surface knot which has a diagram with no triple points by a finite
number of 1-handle additions. The minimum number of such 1-handles is called
the unknotting number or the triple point cancelling number, respectively.
In December 2011, I gave a talk in this seminar on upper bounds and lower
bounds of unknotting numbers of torus-covering knots, which are surface
knots in the form of coverings over the standard torus $T$. In this talk,
we give lower bounds of triple point cancelling numbers of torus-covering
knots, by using Iwakiri's result and calculating quandle cocycle invariants.
In particular, we give examples of torus-covering knots whose unknotting
numbers and triple point cancelling numbers are exactly two. |
| Date |
July 12 (Fri.) 16：00～17：00 |
| Speaker |
Kazuto Takao (Hiroshima University) |
| Title |
Destabilized bridge spheres of knots |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
Any knot admits infinitely many bridge spheres, and to classify them is
a general problem. Destabilized bridge spheres are of particular interest
because all the other can be obtained from them by stabilizations up to
isotopy. In this talk, we introduce a criterion which guarantees a bridge
sphere to be destabilized, and give a knot which has destabilized bridge
spheres of bridge number arbitrarily higher than the bridge number of the
knot. This is a joint work with Yeonhee Jang, Tsuyoshi Kobayashi and Makoto
Ozawa. |
| Date |
July 5 (Fri.) 16：00～17：00 |
| Speaker |
Yuriko Umemoto (Osaka City Univerisity) |
| Title |
Growth rates of cocompact hyperbolic Coxeter groups and
2-Salem numbers |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The group generated by reflections with respect to facets of a Coxeter
polytope in n-dimensional hyperbolic space $\\H^n$ is called a hyperboric
Coxeter group. By the results of Cannon, Wagreich and Parry, it is known
that the growth rate of a cocompact Coxeter group in $\H^2$ and $\H^3$
is a Salem number. On the other hand, Kerada defined a $j$-Salem number,
which is a generalization of a Salem number. In this talk, I will present
that we realize infinitely many 2-Salem numbers as the growth rates of
cocompact Coxeter groups in $\H^4$. Our Coxeter polytopes are constructed
by successive gluing of Coxeter polytopes which we call Coxeter dominoes. |
| Date |
June 28 (Fri.) 16：00～17：00 |
| Speaker |
Tsukasa Yashiro (Sultan Qaboos Univeristy) |
| Title |
Constructing surface-diagrams with cross-exchangeable cycles |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
Roseman moves are local deformations of surface diagrams which are generalized
version of Reidemeister moves of knot diagrams. Each Roseman move requires
geometric conditions. We look at the the move which involves a saddle and
a regular disc. This move changes the number of immersed circles or immersed
intervals in the double decker set. For some diagrams we cannot apply this
move to obtain a different diagram. We call this diagram a d-minimal surface
diagram. On the other hand, we can define a special double curve in a surface
diagram along which we can change the crossing information so that we obtain
a trivial diagram. We call this curve a cross-exchangeable cycle or arc.
In this talk we present a construction of a series of d-minimal surface
diagrams with cross-exchangeable cycles.
This research is a joint work with Abdul Mohamad. |
| Date |
June 21 (Fri.) 16：00～17：00 |
| Speaker |
Tetsuya Ito (RIMS) |
| Title |
Singular spanning discs, framing function of knots, and
strength version of Dehn's lemma |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
Greene-Wiest introduced a framing function of K by counting the intersection
of a singular disc spanned by K. In this talk we explain basics of framing
functions emphasizing interactions with several aspects of knot theory.
We show a lower bound of framing functions and as an application, we give
a slightly generalized version of Dehn's lemma. |
| Date |
June 14 (Fri.) 16：00～17：00 |
| Speaker |
Shin Satoh (Kobe University) |
| Title |
On knots with no 3-state |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
Kauffman introduces the state model for a Jones polynomial, where the number
of circles in each state is an important quantity. For a positive integer
k, a k-state of a (classical or virtual) knot diagram is such a state consisting
of k circles. It is easy to see that any non-trivial diagram has 1- and
2-states both. In this talk, we determine knot diagrams with no 3-states
via Gauss diagrams, and give several properties related to the integer-writhes,
upper and lower knot groups, and Miyazawa polynomials. |
| Date |
June 7 (Fri.) 16：00～17：00 |
| Speaker |
Migiwa Sakurai (Tokyo Woman's Christian University) |
| Title |
An estimate of the unknotting numbers for virtual knots by
forbidden moves |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
It is known that any virtual knot can be deformed into the trivial knot
by a finite sequence of forbidden moves. In this talk, we give the difference
of the values obtained from some invariants constructed by A. Henrich between
two virtual knots which can be transformed into each other by a single
forbidden move. As a result, we obtain a lower bound of the unknotting
number of a virtual knot by forbidden moves. |
| Date |
May 31 (Fri.) 16：00～17：00 |
| Speaker |
Hiromasa Moriuchi（OCAMI） |
| Title |
A table of coherent band-Gordian distances between knots |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
A coherent band surgery is a local move on an oriented link, which is equivalent
to a smoothing a crossing. The coherent band-Gordian distance between two
links is the least number of coherent band surgeries needed to transform
one link into the other. We introduce some criteria for two links which
are related by a coherent band surgery. Then we give a table of coherent
band-Gordian distances between two knots with up to seven crossings.
This is a joint work with Taizo Kanenobu. |
| Date |
May 10 (Fri.) 16：00～17：00 |
| Speaker |
Kenta Hayano (Osaka University) |
| Title |
On four-manifolds with genus-1 simplified broken Lefschetz
fibrations |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
In 2005, Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations
in order to understand near-symplectic structures via fibration structures.
Simplified broken Lefschetz fibrations are broken Lefschetz fibrations
with several conditions on topology and configuration of singularities.
Although negative definite four-manifolds cannot admit near-symplectic
structures, it turns out that every closed, oriented, connected four-manifold
has a simplified broken Lefschetz fibration. In this talk, we first relate
simplified broken Lefschetz fibrations to mapping class groups via monodromy
representations. Using this relation, we then discuss the classification
problem of genus-1 simplified broken Lefschetz fibrations. |
| Date |
April 26 (Fri.) 16：00～17：00 |
| Speaker |
Seiichi Kamada (Osaka City University) |
| Title |
Chart descriptions of 2-dimensional braids |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The chart description was first introduced by the speaker to describe simple
2-dimensional braids. In this talk we consider chart descriptions for non-simple
2-dimensional braids, especially those called "regular". Any
regular 2-dimensional braid can be described by a regular chart, and such
regular descriptions are related by certain moves. |
| Date |
April 19 (Fri.) 16：00～17：00 |
| Speaker |
Hirotaka Akiyoshi (Osaka City University) |
| Title |
Hyperbolic structures on the torus with a single cone point |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
We construct hyperbolic structures on the torus with a single cone point
in a canonical way. It is proved that a variant of McShane's identity holds
for such a structure by Tan-Wong-Zhang, where they developed the study
on generalized Markoff maps and showed that the Bowditch's Q-Condition
(BQ-condition) is crucial for the convergence of the identity. Our proof
uses their results to find a canonical generators for a given real generalized
Markoff map satisfying the BQ-condition. |
| Date |
April 12 (Fri.) 16：00～17：00 |
| Speaker |
Hideo Takioka (Osaka City University) |
| Title |
The cable $\Gamma$-polynomial of a knot |
| Place |
Dept. of Mathematics, General Research Bldg., 401 |
| Abstract |
The $\Gamma$-polynomial is an invariant of an oriented link, which is the
zeroth coefficient polynomial of both the HOMFLYPT polynomial and the Kauffman
polynomial. In particular, we study the cable $\Gamma$-polynomial of a
knot, that is, the $\Gamma$-polynomial of a cable knot. I will talk about
several results of the 2-cable $\Gamma$-polynomials of the Kanenobu knots
and the 3-cable $\Gamma$-polynomial of a mutant knot. |
Last Modified on February 13, 2014
