トポロジー火曜セミナー

開催情報	火曜日　17:00～18:30　数理科学研究科棟(駒場) 056号室
担当者	河澄響矢, 北山貴裕, 逆井卓也, 葉廣和夫
セミナーURL	https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html

2013年12月17日(火)

16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
中村伊南沙氏 (東京大学大学院数理科学研究科)
Satellites of an oriented surface link and their local moves (JAPANESE)

[ 講演概要 ]
For an oriented surface link

$F$ in

$\\mathbb{R}^4$ ,
we consider a satellite construction of a surface link, called a
2-dimensional braid over

$F$ , which is in the form of a covering over

$F$ . We introduce the notion of an

$m$ -chart on a surface diagram

$p(F)\\subset \\mathbb{R}^3$ of

$F$ , which is a finite graph on

$p(F)$
satisfying certain conditions and is an extended notion of an

$m$ -chart on a 2-disk presenting a surface braid.
A 2-dimensional braid over

$F$ is presented by an

$m$ -chart on

$p(F)$ .
It is known that two surface links are equivalent if and only if their
surface diagrams are related by a finite sequence of ambient isotopies
of

$\\mathbb{R}^3$ and local moves called Roseman moves.
We show that Roseman moves for surface diagrams with

$m$ -charts can be
well-defined. Further, we give some applications.

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