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トポロジー火曜セミナー
過去の記録 ～04/24｜次回の予定｜今後の予定 04/25～
| 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 |
2021年01月12日(火)
17:00-18:00 オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
木村 満晃 氏 (東京大学大学院数理科学研究科)
Bounded cohomology of volume-preserving diffeomorphism groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
木村 満晃 氏 (東京大学大学院数理科学研究科)
Bounded cohomology of volume-preserving diffeomorphism groups (JAPANESE)
[ 講演概要 ]
Let M be a complete Riemannian manifold of finite volume. Brandenbursky and Marcinkowski proved that the third bounded cohomology of the volume-preserving diffeomorphism group of M is infinite dimensional when the fundamental group of M is "complicated enough". For example, if M is two-dimensional, the above condition is satisfied if the Euler characteristic is negative. Recently, we have extended this result in the following two directions.
(1) When M is two-dimensional and the Euler characteristic is greater than or equal to zero.
(2) When the volume of M is infinite.
In this talk, we will mainly discuss (1). The key idea is to use the fundamental group of the configuration space of M (i.e., the braid group), rather than the fundamental group of M. If time permits, we will also explain (2). For this extension, we introduce the notion of "norm controlled cohomology".
[ 参考URL ]Let M be a complete Riemannian manifold of finite volume. Brandenbursky and Marcinkowski proved that the third bounded cohomology of the volume-preserving diffeomorphism group of M is infinite dimensional when the fundamental group of M is "complicated enough". For example, if M is two-dimensional, the above condition is satisfied if the Euler characteristic is negative. Recently, we have extended this result in the following two directions.
(1) When M is two-dimensional and the Euler characteristic is greater than or equal to zero.
(2) When the volume of M is infinite.
In this talk, we will mainly discuss (1). The key idea is to use the fundamental group of the configuration space of M (i.e., the braid group), rather than the fundamental group of M. If time permits, we will also explain (2). For this extension, we introduce the notion of "norm controlled cohomology".
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
