| Date |
February 3 (Fri.) 16：00～17：00 |
| Speaker |
Kumi Kobata（OCAMI） |
| Title |
A generalization of an enumeration on cyclic automorphism graphs
for edge colored hypergraphs |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
We plan to give a generalization of Ohno's theorem for hypergraphs which
gives a formula for enumeration on cyclic automorphism graphs with given
number of vertices. We consider the enumeration in case of edge colored
hypergraphs. This is a joint work with Yasuo Ohno. |
| Date |
February 3 (Fri.) 15：00～16：00 |
| Speaker |
Chad Musick (Nagoya University) |
| Title |
Recognizing Trivial Links in Polynomial Time |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
Trivial links are unique up to number of link components, but they can
be hard to recognize from arbitrary diagrams. We define a measure, the
crumple, on link diagrams and then demonstrate that for trivial links there
is a sequence of moves by which the crumple may be strictly monotonically
reduced. By our definition, the minimum possible crumple over all link
diagrams is achieved only by embedding components disjointly in parallel
planes, and so a link will be able to obtain this crumple if and only if
it is trivial. The crumple is quadratic in the number of crossings, and
we show that finding each reducing move takes only polynomial time and
linear space. Therefore, we may decide whether a link is trivial in time
polynomial on the number of crossings of a diagram of the link.
arXiv: 1110.2871v1 [math.GT] |
| Date |
January 27 (Fri.) 16：00～17：00 |
| Speaker |
Kanako Oshiro (Japan Women's University) |
| Title |
Minimal numbers of colors for surface-knots and quandle cocycle
invariants |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
We study the minimal number of colors used for non-trivial Fox colorings
of surface-knots. A lower bound for the minimal number is given by using
quandle cocycle invariants. In particular, we show that the minimal number
of the $2$-twist spinning of the $5_2$ knot for Fox 7-colorings is six.
This is a joint work with Shin Satoh (Kobe University). |
| Date |
January 27 (Fri.) 15：00～16：00 |
| Speaker |
Reiko Shinjo (Waseda University) |
| Title |
On the collection of complementary faces associated to the diagrams of
a link
(partially joint work with Colin C. Adams and Kokoro Tanaka) |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
Given a diagram of a link, one can ignore which strand is the overstrand
at each crossing and think of it as a planar $4$-valent graph embedded
on the $2$-sphere. This graph divides the sphere into $n$-gons, which we
call faces. In this talk, we investigate the possibilities for the collection
of complementary $n$-gon faces associated to the diagrams of a link. |
| Date |
December 16 (Fri.) 16：00～17：00 |
| Speaker |
Roland van der Veen（University of California, Berkeley） |
| Title |
The many faces of the colored Jones polynomial |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
In this talk we will discuss an elementary definition of the colored Jones
polynomial for knots and show how it relates to many other aspects of knot
theory. In particular we will give a survey of conjectures on the colored
Jones polynomial including the volume conjecture and the AJ conjecture
and report on recent progress. |
| Date |
December 16 (Fri.) 15：00～16：00 |
| Speaker |
Inasa Nakamura (RIMS, Kyoto University) |
| Title |
Unknotting numbers of torus-covering knots |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
A torus-covering knot is an oriented surface knot which is in the form
of a covering over the standard torus. The unknotting number of an oriented
surface knot $F$ is the minimal number of disjoint 1-handles necessary
to deform $F$ to an unknotted surface knot by 1-handle surgery. In this
talk we study unknotting numbers of torus-covering knots. In particular,
we give examples of torus-covering knots with the unknotting number exactly
$n$. |
| Date |
December 9 (Fri.) 16：00～17：00 |
| Speaker |
Kazuto Takao (Osaka University) |
| Title |
Heegaard splittings and singularities of product maps |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
We give an upper bound for the Reidemeister-Singer distance between two
Heegaard splittings in terms of the genera plus a somewhat unexpected number.
It is unfortunately ambiguous but suggests that a certain development in
singularity theory may lead to the best possible bound for the Reidemeister-Singer
distance. |
| Date |
November 25 (Fri.) 16：00～17：00 |
| Speaker |
Naoyuki Monden (Osaka University) |
| Title |
Surface bracket polynomials of twisted links |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
We will discuss the possible self-intersection numbers for sections of
surface bundles & Lefschetz fibrations over surfaces, and the (un)boundedness
of the number of critical points of a Lefschetz fibration with maximally
self-intersecting sections, for fixed fiber and base genera. We will also
calculate the stable commutator length of certain elements in the mapping
class groups of surfaces with boundary. |
| Date |
November 18 (Fri.) 16：00～17：00 |
| Speaker |
Masahide Iwakiri (Saga University) |
| Title |
On $3$-component surface-links with braid index $4$ |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
Any surface-links with braid index at most $3$ are ribbon, and any $m$-component
surface-links with braid index $m$ are trivial $2$-links. There are examples
of non-ribbon $1$- or $2$-component $2$-links with braid index $4$. In
this talk, we show that any $3$-component surface-links with braid index
$4$ are ribbon. |
| Date |
November 11 (Fri.) 16：00～17：00 |
| Speaker |
Takahiro Miura (Kobe University) |
| Title |
On flat braidzel surfaces for links |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
Rudolph introduced a notion of braidzel surfaces as a generalization of
pretzel surfaces in his study on quasipositivity for pretzel surfaces,
and Nakamura showed that any oriented link has a braidzel surface as a
Seifert surface for the link. In this talk, we introduce the notion of
flat braidzel surfaces as a special kind of braidzel surfaces, and show
that any oriented link has a flat braidzel surface. Moreover, we also introduce
the genus and the crossing number of bands with respect to flat braidzel
surfaces, and study their properties. |
| Date |
November 4 (Fri.) 16：00～17：00 |
| Speaker |
Yoshiro Yaguchi (Hiroshima University) |
| Title |
Homological invariants of systems of simple braids |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
Hurwitz equivalence on systems of simple braids is studied, which can be
used in the study of surface braids and surface links. In this talk, we
define a matrix for a system of simple braids by using the first homology
classes of a punctured disk. As applications, we give some invariants of
surface braids by using the matrices obtained from the systems of their
braid monodromies. |
| Date |
October 28 (Fri.) 16：00～17：00 |
| Speaker |
Tetsuya Abe (RIMS, Kyoto University) |
| Title |
Unoriented band-surgery on knots and links |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
A band-surgery is a local move on knots and links. It is well known that
a band-surgery is an unknotting operation. In this talk, we survey some
results on band-surgeries, and study how the orientability of a band-surgery
relates to its unknotting sequences when we unknot a given knot by band-surgeries.
This is a joint work with Taizo Kanenobu. |
| Date |
October 21 (Fri.) 16：00～17：00 |
| Speaker |
Tatsuya Tsukamoto (Osaka Institute of Technology) |
| Title |
Simple ribbon fusions for links |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
We define and study special kinds of fusions, called simple ribbon fusions,
for a link and a trivial link. A simple ribbon move, which we have previously
worked on, is a simple ribbon fusion. Main theorem gives a sufficient condition
for a knot obtained from the trivial knot by a simple fusion to be non-trivial.
As a corollary, we show that the Kinoshita-Terasaka knot is non-trivial.
This is a joint work with K.Kishimoto and T.Shibuya. |
| Date |
October 7 (Fri.) 16：00～17：00 |
| Speaker |
Yukari Funakoshi (Nara Women's University) |
| Title |
On pseudo-fiber surfaces of level $n$ |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
The concept of pre-fiber surface in the 3-sphere $S^3$ was introduced by
Kobayashi in [Ko]. In the paper, it is shown that any pre-fiber surface
is transformed into a fiber surface by twisting is along arcs with certain
properties. In this talk, we introduce pseudo-fiber surfaces of level $n$
for each non-negative integer $n$. (We note that a surface is a fiber surface
if and only if it is a pseudo-fiber surface of level 0, and it is a pre-fiber
surface if and only if it is a pseudo-fiber surface of level 1.) We show
some fundamental properties of pseudo-fiber surfaces. Then we show that
if an arc proper embedded in a pseudo-fiber surface of level $n$ satisfies
certain properties, then the twist along the arc transforms it into a pseudo-fiber
surface of level $n-1$. This gives a natural generalization of a result
of Kobayashi's. Finally we propose an application of pseudo-fiber surface
for giving an estimation of unknotting numbers of fibered knots. |
| Date |
July 15 (Fri.) 16：00～17：00 |
| Speaker |
Takefumi Nosaka (RIMS, Kyoto University) |
| Title |
Quandle cocycle invariants of Lefschetz fibrations over the 2-sphere |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
We introduce quandle cocycle invariants of 4-dimensional Lefschetz fibrations
over the 2-sphere, using quandle cocycles of Dehn quandles with non-abelian
coefficients. In this talk, we first review a topological interpretation
of quandle 2-cocycle invariants for links in $S3$ shown by M. Eisermann.
We next present a 2-cocycle so that the associated invariant is equivalent
to the signature of 4-dimensional manifolds. |
| Date |
July 8 (Fri.) 16：00～17：00 |
| Speaker |
Sosuke Ashihara (Hiroshima University) |
| Title |
Biquandle presentations of surface links from ch-diagrams |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
A biquandle is a set with four binary operations which satisfy some axioms
corresponding to Reidemeister moves. A surface link is a closed oriented
surface embedded in four-space. It is known that a biquandle gives an invariant
for a surface link and any surface link is presented by a link diagram
with some markers which is called a ch-diagram. The speaker gives a method
that we directly calculate the biquandle of a surface link from a ch-diagram
presenting the surface. |
| Date |
July 8 (Fri.) 15：00～16：00 |
| Speaker |
Yoriko Kodani (Nara Women's University) |
| Title |
A new bridge index for links with trivial knot components |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
In 1954, H. Schubert introduced the concept of bridge indices for knots.
For satellite knots, he gave an estimation of bridge indices by using index
of the pattern and the bridge index of the companion of the satellite knot
under consideration. In 2003, J.Schultens gave a modern proof of the result
by using foliation.
In this talk, we consider bridge indices of links. We introduce a new bridge
index for non-split 2-component links such that one component of each link
is a trivial knot. Roughly speaking, the bridge index is the minimum of
the bridge numbers of a link under the constraint that one component of
the link is in a minimal bridge position. We give an estimation of the
bridge index for satellite links by using the technique of Schultens'.
We show, by using the estimation, the new bridge index is essentially different
from the standard one. |
| Date |
July 1 (Fri.) 16：00～17：00 |
| Speaker |
Ryokichi Tanaka (Kyoto University) |
| Title |
Penner-Andersen's Fatgraph Models of Proteins |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
In 2009, R.C.Penner and J.E.Andersen proposed to classify conformations
of proteins by using topological invariants. They introduced the Fatgraph
for modeling proteins and constructed an algorithm to calculate those invariants.
Their methods are suitable for computation and existing database implies
that their invariants could be useful for structural classification of
proteins. I would like to introduce their methods and also propose some
questions. |
| Date |
June 24 (Fri.) 16：00～17：00 |
| Speaker |
Taizo Kanenobu (Osaka City University) |
| Title |
Band surgery on 2-component links |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
An oriented 2-component link is called band-trivializable, if it can be
unknotted by a single band surgery. We consider whether a given 2-component
link is band-trivializable or not. Then we can completely determine the
band-trivializability for the prime links with up to 9 crossings. We use
the signature, the Jones and Q polynomials, and the Arf invariant. Since
a band-trivializable link has 4-ball genus zero, we also give a table for
the 4-ball genus of the prime links with up to 9 crossings. Furthermore,
we give an additional answer to the problem of whether a $(2n+1)$-crossing
2-bridge knot is related to a $(2,2n)$ torus link or not by a band surgery
for $n=3$, $4$, which was brought from the study of a DNA site-specific
recombination. |
| Date |
June 17 (Fri.) 16：00～17：00 |
| Speaker |
Tsukasa Yashiro (Sultan Qaboos University) |
| Title |
Cell-complexes for surface diagrams and Roseman moves |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
A surface-knot is a connected oriented closed surface embedded in 4-space.
If we project a surface-knot in 3-space, then we obtain a surface diagram
that may have double points or triple points or branch points. The preimage
of the set of multiple points is the union of two families of connected
components called the upper and lower double decker set. The lower decker
set induces a cell-complex for the surface diagram. There is a set of local
deformations of the cell-complex induced from Roseman moves. In this talk
we discuss about a relation between these local moves and cell-complexes. |
| Date |
June 10 (Fri.) 16：00～17：00 |
| Speaker |
Takanori Imabeppu (Hiroshima University) |
| Title |
On normalized arrow polynomials of checkerboard colorable virtual links |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
It is known that every classical knot diagram is checkerboard colorable,
but every virtual knot diagram is not checkerboard colorable. Normalized
arrow polynomials introduced by Kauffman are a generalization of Jones
polynomials. We show that some virtual links are not checkerboard colorable
by using a certain property of normalized arrow polynomials. |
| Date |
June 3 (Fri.) 16：00～17：00 |
| Speaker |
Takahito Kuriya（OCAMI） |
| Title |
Mosaic quantum knots and related topics |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
In a recent work of Samuel J. Lomonaco Jr and Louis H. Kauffman, they consider
the concept of mosaic quantum knots in the context of quantum graphs. We
review mosaic knot theory and introduce related topics and our recent results. |
| Date |
May 20 (Fri.) 16：00～17：00 |
| Speaker |
Kenta Hayano (Osaka University) |
| Title |
Classification of genus-1 simplified broken Lefschetz |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
Broken Lefschetz fibrations were introduced as a generalization of Lefschetz
fibrations to near-symplectic setting. In this talk, we first construct
a family of genus-1 simplified broken Lefschetz fibrations. We then show
that all genus-1 simplified broken Lefschetz fibrations with small number
of Lefschetz singularities are contained in the family we construct. |
| Date |
May 13 (Fri.) 16：00～17：00 |
| Speaker |
Yeonhee Jang (Hiroshima University) |
| Title |
Bridge presentations of links and Heegaard splittings of 3-manifolds |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
It is known that bridge presentations of links in the 3-sphere are deeply
related with Heegaard splittings of 3-manifolds. The speaker has used this
relation and studied Heegaard splittings of certain 3-manifolds to obtain
several results on bridge presentations of links. In this talk, we give
a brief survey on the results and show you how to use the relation. |
| Date |
April 22 (Fri.) 16：00～17：00 |
| Speaker |
Ikuo Tayama（OCAMI） |
| Title |
Enumerating 3-manifolds with the first homology groups
isomorphic to (Z/nZ)+(Z/nZ) with lengths up to 10 |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
This is a joint work with A. Kawauchi. A well-order was introduced on the
set of links by A. Kawauchi. This well-order also naturally induces a well-order
on the set of prime link exteriors and eventually induces a well-order
on the set of closed connected orientable $3$-manifolds. With respect to
this order, we enumerated the prime links and the prime link exteriors
with lengths up to 10. In this talk, we show a list of the enumeration
of $3-$manifolds with the first homology groups isomorphic to (Z/nZ)+(Z/nZ)
with lengths up to 10 by using the enumeration of the prime link exteriors. |
| Date |
April 15 (Fri.) 16：00～17：00 |
| Speaker |
Tetsuya Ito (The University of Tokyo) |
| Title |
Links having non-left orderable 2-fold branched coverings |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
The (left) orderability of 3-manifold groups is closely related to the
existence of certain foliations or laminations. Recently, it is observed
that the left-orderbility is also related to Heegaard Floer homologies.
Thus it is interesting to construct examples of 3-manifolds having non-
left orderable fundamental group. In this talk I will give a family of
links whose 2-fold branched covering has non-left orderable fundamental
group. |
| Date |
April 8 (Fri.) 16：00～17：00 |
| Speaker |
Ayaka Shimizu（OCAMI） |
| Title |
Region crossing change is an unknotting operation |
| Place |
Dept. of Mathematics, Sci. Bldg., 3153 |
| Abstract |
K. Kishimoto proposed a new local transformation on a knot or link diagram
called a region crossing change. In this talk, we show that a region crossing
change on a knot diagram is an unknotting operation, and we define the
region unknotting numbers for a knot diagram and a knot. |
Last Modified on January 30, 2012
