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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 |
今後の予定
2026年06月23日(火)
16:00-17:30 数理科学研究科棟(駒場) hybrid/056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。
Andrei Pajitnov 氏 (Université de Nantes)
Morse-Novikov theory for links (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。
Andrei Pajitnov 氏 (Université de Nantes)
Morse-Novikov theory for links (ENGLISH)
[ 講演概要 ]
Let M be a compact manifold with a non-empty boundary N, and x an element of the first cohomology group of M. We assume that the restriction of x to N can be represented by a fibration over a circle. The Morse-Novikov number MN(M,x) is the minimal possible number of critical points of a Morse map f of M to a circle, such that [f]=x, and the restriction of f to N is a fibration over the circle. In this talk we present our results about the Morse-Novikov numbers for the exteriors of links in 3-sphere. This is joint work with L. Chen and H. Endo.
[ 参考URL ]Let M be a compact manifold with a non-empty boundary N, and x an element of the first cohomology group of M. We assume that the restriction of x to N can be represented by a fibration over a circle. The Morse-Novikov number MN(M,x) is the minimal possible number of critical points of a Morse map f of M to a circle, such that [f]=x, and the restriction of f to N is a fibration over the circle. In this talk we present our results about the Morse-Novikov numbers for the exteriors of links in 3-sphere. This is joint work with L. Chen and H. Endo.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.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
2026年07月07日(火)
16:00-17:00 オンライン開催
セミナーのホームページから参加登録を行って下さい。
矢ヶ崎 達彦 氏 ( 京都工芸繊維大学)
Topological properties of groups of volume-preserving diffeomorphisms and groups of uniform homeomorphisms (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
セミナーのホームページから参加登録を行って下さい。
矢ヶ崎 達彦 氏 ( 京都工芸繊維大学)
Topological properties of groups of volume-preserving diffeomorphisms and groups of uniform homeomorphisms (JAPANESE)
[ 講演概要 ]
This talk is a continuation of survey on topological properties of groups of homeomorphisms/diffeomorphisms on noncompact manifolds. As a subject related to ends of noncompact manifolds, we discuss volume transfer towards ends, which leads to the existence of continuous sections under the compact-open topology for the actions of diffeomorphism groups on the spaces of volume forms on noncompact manifolds (a noncompact version of Moser's theorem) and for the end charge homomorphisms introduced by Alpern and Prasad. We also give a brief survey on the local and end deformation properties in groups of uniform homeomorphisms on noncompact metric manifolds with the sup-metric.
[ 参考URL ]This talk is a continuation of survey on topological properties of groups of homeomorphisms/diffeomorphisms on noncompact manifolds. As a subject related to ends of noncompact manifolds, we discuss volume transfer towards ends, which leads to the existence of continuous sections under the compact-open topology for the actions of diffeomorphism groups on the spaces of volume forms on noncompact manifolds (a noncompact version of Moser's theorem) and for the end charge homomorphisms introduced by Alpern and Prasad. We also give a brief survey on the local and end deformation properties in groups of uniform homeomorphisms on noncompact metric manifolds with the sup-metric.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
