# Category:トポロジーセミナー

## トポロジーセミナー（2017/09/21）

In particular, some invariants from biquandles are known to be stronger than those from quandles for virtual links.

In this talk, we first explain that, for any classical/surface link, we can recover (a biquandle isomorphic to) the fundamental biquandle from the fundamental quandle.
This result implies that many biquandle invariants are reduced to quandle ones.
In fact, a biquandle coloring number is equal to a quandle coloring number.
Furthermore, we give an explicit one-to-one correspondence between biquandle colorings and quandle colorings.
As a corollary, a biquandle cocycle invariant is described by a quandle shadow cocycle invariant.

This is a joint work with Kokoro Tanaka (Tokyo Gakugei University).

## トポロジーセミナー（2017/09/04）

アブストラクト：We give infinitely many examples of closed, orientable, irreducible 3-manifolds $M$ such that $b_1(M)=1$ and $\pi_1(M)$ has weight 1, but $M$ is not the result of Dehn surgery along a knot in the 3-sphere.
This answers a question of Aschenbrenner, Friedl and Wilton.
This is joint work with Matt Hedden and Kyungbae Park.

## トポロジーセミナー（2017/09/04）

アブストラクト：Cappell と Shaneson は、３次元トーラスの mapping torus を手術することにより４次元のホモトピー球面を無数に構成する方法を示した。
Gompf はこのホモトピー球面の微分同相型を固定したまま、mapping torus の貼り合わせ写像（およびそれに対応する行列）を取りかえる操作を新たに導入した。

なお、この研究は Min Hoon Kim 氏との共同研究である。

## トポロジーセミナー（2017/06/28）

アブストラクト：測地流の一般化としてリーマン多様体上の磁場軌道が研究されている．３次元多様体の接触構造から自然に定まる磁場軌道の周期性に関する成果を報告する．（M.I.Munteanu氏との共同研究）

## トポロジーセミナー（2017/04/27）

アブストラクト：For metric spaces, the doubling property, the uniform disconnectedness, and the uniform perfectness are known as quasi-symmetric invariant properties.
We say that a Cantor metric space is standard if it satisfies all the three properties; otherwise, it is exotic.
For instance, the middle-third Cantor set is standard.
In this talk, we discuss our constructions of exotic Cantor metric spaces for all the possible cases of satisfying each of the three properties or not.
Our constructions enable us to classify Cantor metric spaces into eight types with concrete examples.
The David-Semmes uniformization theorem tells us that standard Cantor metric spaces are quasi-symmetric equivalent.
In this talk, we conclude that there exist at least two exotic Cantor metric spaces of the same type that are not quasi-symmetric equivalent to each other.
Moreover, for each of all the non-uniformly disconnected types, there exist at least aleph one many quasi-symmetric equivalent classes of Cantor metric spaces of such a given type.
As a byproduct of our study, we state that there exists a Cantor metric space with prescribed Hausdorff dimension and Assoud dimension.