トポロジー火曜セミナー

過去の記録 ~03/28次回の予定今後の予定 03/29~

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
セミナーURL http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html

2009年03月05日(木)

16:30-18:00   数理科学研究科棟(駒場) 056号室
いつもと曜日が異なります. Tea: 16:00 - 16:30 コモンルーム
Shicheng Wang 氏 (Peking University)
Extending surface automorphisms over 4-space
[ 講演概要 ]
Let $e: M^p\\to R^{p+2}$ be a co-dimensional 2 smooth embedding
from a closed orientable manifold to the Euclidean space and $E_e$ be the subgroup of ${\\cal M}_M$, the mapping class group
of $M$, whose elements extend over $R^{p+2}$ as self-diffeomorphisms. Then there is a spin structure
on $M$ derived from the embedding which is preserved by each $\\tau \\in E_e$.

Some applications: (1) the index $[{\\cal M}_{F_g}:E_e]\\geq 2^{2g-1}+2^{g-1}$ for any embedding $e:F_g\\to R^4$, where $F_g$
is the surface of genus $g$. (2) $[{\\cal M}_{T^p}:E_e]\\geq 2^p-1$ for any unknotted embedding
$e:T^p\\to R^{p+2}$, where $T^p$ is the $p$-dimensional torus. Those two lower bounds are known to be sharp.

This is a joint work of Ding-Liu-Wang-Yao.