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# トポロジーセミナー（2017/09/21）

日時：2017年9月21日（木）15：15〜16：15

場所：筑波大学 自然系学系D棟D814

講演者：石川勝巳 氏 （京都大学 数理解析研究所）

講演題目：A relation between biquandle coloring and quandle coloring

アブストラクト：As well as quandles, biquandles give many invariants for links, virtual links, and higher dimensional links.

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

However, we have not found an essentially refined invariant for classical 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).

場所：筑波大学 自然系学系D棟D814

講演者：石川勝巳 氏 （京都大学 数理解析研究所）

講演題目：A relation between biquandle coloring and quandle coloring

アブストラクト：As well as quandles, biquandles give many invariants for links, virtual links, and higher dimensional links.

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

However, we have not found an essentially refined invariant for classical 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).