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トポロジー火曜セミナー
過去の記録 ～06/20｜次回の予定｜今後の予定 06/21～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 池 祐一, 今野 北斗, 逆井卓也 |
| セミナーURL | https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2026年06月30日(火)
16:00-17:30 数理科学研究科棟(駒場) hybrid/123号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Sang-hyun Kim 氏 (Korea Institute For Advanced Study)
Structure and rigidity of manifold diffeomorphism groups (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Sang-hyun Kim 氏 (Korea Institute For Advanced Study)
Structure and rigidity of manifold diffeomorphism groups (ENGLISH)
[ 講演概要 ]
Given a manifold M and a structure S, we denote by Homeo(M;S) the group of S-preserving homeomorphisms of M. We will be particularly concerned with the case tha S is the C^r structure in the sense of Hölder continuity. In such a case, the group is written as Diff^r(M). The goal of this lecture series is to survey recent results and open questions on the rigidity of the group structures involving these groups. When M is a compact one-manifold, namely an interval or a circle, each real number r≥1 admits a finitely generated subgroup G_r of Diff^r(M) such that G_r never embeds into Diff^s(M) for any s>r. This generalizes observations by earlier foliation theorists on the case r=0 or r=1. In the second talk, I will propose a rigidity phenomenon regarding higher dimensional manifolds. Namely, we consider the question exactly when two manifold diffeomorphism groups Diff^r(M) and Diff^s(N) have the same logical structure. Modern findings regarding this question gives a generalization of classical results of Whittaker (1963), and of Takens-Filipkiewicz (1982). This talk is based on joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS).
[ 参考URL ]Given a manifold M and a structure S, we denote by Homeo(M;S) the group of S-preserving homeomorphisms of M. We will be particularly concerned with the case tha S is the C^r structure in the sense of Hölder continuity. In such a case, the group is written as Diff^r(M). The goal of this lecture series is to survey recent results and open questions on the rigidity of the group structures involving these groups. When M is a compact one-manifold, namely an interval or a circle, each real number r≥1 admits a finitely generated subgroup G_r of Diff^r(M) such that G_r never embeds into Diff^s(M) for any s>r. This generalizes observations by earlier foliation theorists on the case r=0 or r=1. In the second talk, I will propose a rigidity phenomenon regarding higher dimensional manifolds. Namely, we consider the question exactly when two manifold diffeomorphism groups Diff^r(M) and Diff^s(N) have the same logical structure. Modern findings regarding this question gives a generalization of classical results of Whittaker (1963), and of Takens-Filipkiewicz (1982). This talk is based on joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
