| Date |
February 10 (Fri.) 16：00～17：30 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Speaker |
16：00～16：30
Celeste Damiani (Osaka City University, JSPS) |
| Title |
The many faces of Loop Braid Groups |
| Abstract |
Loop braid groups, are a generalization of braid groups. These
groups have been an object of interest in different domains of mathematics
and mathematical physics, and have been called, in addition to loop braid
groups, with several names such as of motion groups, groups of
permutation-conjugacy automorphisms, braid-permutation groups, welded braid
groups and untwisted ring groups. We unify all the formulations that have
appeared so far in the literature, with a complete proof of the equivalence
of these definitions. We also introduce an extension of these groups that
appears to be a more natural generalization of braid groups from the
topological point of view. |
| Speaker |
16：30～17：00
Jieon Kim (Osaka City University, JSPS) |
| Title |
Marked graph diagrams of immersed surface-links |
| Abstract |
An immersed surface-link is the image of the disjoint union of
oriented surfaces in the 4-space $\mathbb R^4$ by a smooth immersion. By
using normal forms of immersed surface-links defined by S. Kamada and K.
Kawamura, we define marked graph diagrams of immersed surface-links. In
addition, we generalize Yoshikawa moves for marked graph diagrams of
surface-links to local moves for marked graph diagrams of immersed
surface-links. We give some examples of marked graph diagrams of immersed
surface-links. This is a joint work with S. Kamada, A. Kawauchi and S. Lee. |
| Speaker |
17：00～17：30
Maria de los Angeles Guevara Hernandez（Instituto Potosino de
Investigacion Cientifica y Tecnologica, and Osaka City University） |
| Title |
Infinite families of prime knots with alternation number $1$ and
dealternating number $n$. |
| Abstract |
The alternation number of a knot $K$, denoted by $alt(K)$, is the
minimum number of crossing changes necessary to transform a diagram of $K$
into some (possibly non-alternating) diagram of an alternating knot. And
the dealternating number of a knot $K$, denoted by $dalt(K)$, is the
minimum number of crossing changes necessary to transform a diagram $D$ of
$K$ into an alternating diagram. So, from these definitions it is immediate
that $alt(K) \leq dalt(K)$ for any knot $K$. In this talk, we will show
that for each positive integer $n$ there exists a family of infinitely
many hyperbolic prime knots with alternation number 1 and dealternating
number $n$. |
| Date |
January 27 (Fri.) 16：00～17：00 |
| Speaker |
Atsushi Ishii (University of Tsukuba) |
| Title |
On augmented Alexander matrices |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We introduce augmented Alexander matrices, and construct link invariants. An augmented Alexander matrix is defined with an Alexander triple, which gives an extension of a quandle. This framework gives the twisted Alexander invariant and the quandle cocycle invariant. This is a joint work with Kanako Oshiro. |
| Date |
January 13 (Fri.) 16：00～17：00 |
| Speaker |
Naoki Sakata (Hiroshima University) |
| Title |
Veering triangulations of mapping tori of some pseudo-Anosov maps arising from Penner's construction |
| 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, I will describe the veering triangulations of the mapping tori of some pseudo-Anosov maps arising from Penner's construction. |
| Date |
December 9 (Fri.) 16：00～17：00 |
| Speaker |
Takuya Ukida (Tokyo Institute of Technology) |
| Title |
Planar Lefschetz fibrations and Stein structures with distinct Ozsvath-Szabo
invariants on corks |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Thanks to a result of Lisca and Matic and a refinement by Plamenevskaya,
it is known that on a 4-manifold with boundary Stein structures with
non-isomorphic $Spin^c$ structures induce contact structures with distinct Ozsvath-Szabo invariants.
Here we give an infinite family of examples showing that converse of
Lisca-Matic-Plamenevskaya
theorem does not hold in general.
Our examples arise from Mazur type corks. |
| Date |
December 2 (Fri.) 16：00～17：00 |
| Speaker |
Shin Satoh (Kobe University, Graduate School of Science, Department of Mathematics) |
| Title |
The ribbon stable class of a surface-link |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Two orientable surface-links are called stably equivalent if they are ambient
isotopic in $4$-space up to adding or deleting trivial $1$-handles. In
this talk, we construct a map $\omega$ from the set of orientable surface-links
to that of stable equivalence classes of ribbon surface-links, and study
several properties of $\omega$. In particular, we prove that $\omega(F)=[F]$
for any ribbon surface-link $F$, that $F$ and $\omega(F)$ have the same
fundamental quandle, that $\omega(F)$ has a representative of genus $1$
for any deform-spinning of a $2$-bridge knot, and that $\omega(\tau^0 L)=\omega(\tau^1
L)$ for any link $L$, where $\tau^k L$ is the $k$-turned spinning of $L$. |
| Date |
November 18 (Fri.) 16：00～17：00 |
| Speaker |
Takefumi Nosaka (Kyushu University, Faculty of Mathematics) |
| Title |
Milnor invariants via unipotent Magnus embeddings |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We reconfigure Milnor invariant, in terms of central group extensions
and unipotent Magnus embeddings, and develop a diagrammatic computation
of the invariant. In this talk, we explain the reconfiguration and
the computation with mentioning some examples. This is a joint work
with Hisatoshi Kodani. |
| Date |
November 4 (Fri.) 16：00～17：00 |
| Speaker |
Tetsuya Ito (Osaka University) |
| Title |
Bi-ordering and Alexander invariants |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We show that if a knot group (more generally, finitely presented group)
is bi-orderable then its Alexander polynomial has at least one positive
real root. |
| Date |
October 28 (Fri.) 16：00～17：00 |
| Speaker |
Katsumi Ishikawa (Research Institute for Mathematical Sciences, Kyoto University) |
| Title |
On the classification of smooth quandles |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A smooth quandle is a differentiable manifold with a smooth quandle
operation.
We show that every smooth transitive connected quandle is
isomorphic to a homogeneous space with an operation defined from a group
automorphism.
We also give an explicit classification of such quandles of dimension 1 and
2. |
| Date |
October 21 (Fri.) 15：00～16：00 |
| Speaker |
Genki Omori (Tokyo Institute of Technology) |
| Title |
A small normal generating set for the handlebody subgroup of the
Torelli group |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We consider the handlebody subgroup of the Torelli group, i.e. the
intersection of the handlebody group and the Torelli group of an orientable
surface. The handlebody subgroup of the Torelli group is related to
integral homology 3-spheres through the Heegaard splittings. In this talk,
we give a small normal generating set for the handlebody subgroup of the
Torelli group. |
| Date |
July 22 (Fri.) 16：00～17：00 |
| Speaker |
Teruhisa Kadokami (Kanazawa University) |
| Title |
Three amphicheiralities of a virtual link |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We define three amphicheiralities for a virtual link by
using its geometric realization. |
| Date |
July 15 (Fri.) 16：00～17：00 |
| Speaker |
Yuta Nozaki (The University of Tokyo) |
| Title |
An explicit relation between knot groups in lens spaces and those in $S^3$ |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We consider a $p$-fold cyclic covering map $(S^3, K) \to
(L(p,q), K')$ and describe the knot group $\pi_1(S^3 \setminus K)$ in
terms of $\pi_1(L(p,q) \setminus K')$. As a consequence, we give an
alternative proof for the fact that a certain knot in $S^3$ cannot be
represented as the preimage of any knot in a lens space. In the proof,
the subgroup of a group $G$ generated by the commutators and the $p$th
power of each element of $G$ plays a key role. |
| Date |
June 24 (Fri.) 16：00～17：00 |
| Speaker |
Tsukasa Yashiro（Suntan Qaboos University, Oman） |
| Title |
Pseudo-cycles of surface-knots and their applications |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A surface-knot is a closed oriented surface smoothly embedded in 4-space.
A surface-knot diagram of a surface-knot is the projected image in 3-space
under the orthogonal projection with crossing information. The pre-image
of multiple point sets of a surface-knot diagram is called a double decker
set that is the union of lower and upper decker sets. The lower decker
set induces a complex consisting of rectangular cells. In this talk we
define pseudo-cycles in the complex. We prove that for a fixed quandle,
the maximal number of pseudo-cycles for all colourings is an invariant
under Roseman moves up to the quandle homology. As its application, we
discuss about the triple point number of some surface-knots. |
| Date |
June 17 (Fri.) 16：00～17：00 |
| Speaker |
Hiroki Murakami (Tokyo Institute of Technology) |
| Title |
Alternating links and root polytopes |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
In this talk, a relationship between the determinant of an alternating link and a certain polytope obtained from the link diagram is presented. Concretely, we show that the volume of the obtained polytope is proportional to the determinant if the given link is alternating. |
| Date |
May 27 (Fri.) 16：00～17：00 |
| Speaker |
Kodai Wada（Waseda University） |
| Title |
Milnor invariants of covering links |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
We consider Milnor invariants for certain covering links as a generalization of covering linkage invariants formulated by R. Hartley and K. Murasugi. A set of Milnor invariants for covering links is a cobordism invariant of a link, and that this invariant can distinguish some links for which the ordinary Milnor invariants coincide.Moreover, for a Brunnian link $L$, the first non-vanishing Milnor invariants of $L$ is modulo-$2$ congruent to a sum of Milnor invariants of covering links. As a consequence, a sum of linking numbers of "iterated" covering links gives the first non-vanishing Milnor invariant of $L$ modulo $2$. This talk is a joint work with Natsuka Kobayashi and Akira Yasuhara. |
| Date |
May 13 (Fri.) 16：00～17：00 |
| Speaker |
Sang Youl Lee (Pusan National University) |
| Title |
The quantum $A_2$ polynomial for oriented virtual links |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A tangled trivalent graph diagram is an oriented link diagram possibly
with some trivalent vertices whose incident edges are oriented all inward
or all outward. Two tangled trivalent graph diagrams are said to be regular
isotopic if they are transformed into each other by a finite sequence of
classical Reidemeister moves of type 2, type 3 and trivalent vertex passing
moves. In 1994, G. Kuperberg derived an inductive, combinatorial definition
of a polynomial-valued regular isotopy invariant (called the quantum $A_2$
invariant) of links and tangled trivalent graph diagrams with values in
the integral Laurent polynomial ring $\mathbb Z[a, a^{-1}]$ that equals
the Reshetikhin-Turaev invariant corresponding to the simple Lie algebra
$A_2$. In this talk, I would like to talk about an extension of the quantum
$A_2$ invariant to virtual tangled trivalent graph diagrams and a derived
polynomial invariant for oriented virtual links satisfying a certain skein
relation. |
| Date |
April 8 (Fri.) 16：00～17：00 |
| Speaker |
Akio Kawauchi (OCAMI) |
| Title |
On a cross-section of an immersed sphere-link in 4-space |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
The torsion Alexander polynomial, the reduced torsion Alexander polynomial and the local signature invariant of a cross-section of an immersed sphere-link are investigated from the viewpoint of how to influence to the immersed sphere-link. It is shown that the torsion Alexander polynomial of a symmetric middle cross-section of a ribbon sphere-link is an invariant of the ribbon sphere-link. A generalization to a symmetric middle cross-section of an immersed ribbon sphere-link is given. |
Last Modified on February 7, 2017
