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トポロジー火曜セミナー
過去の記録 ～07/26｜次回の予定｜今後の予定 07/27～
| 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 |
2025年07月08日(火)
17:00-18:30 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。
石倉 宙樹 氏 (東京大学大学院数理科学研究科)
Stallings-Swan’s Theorem for Borel graphs (JAPANESE)
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。
石倉 宙樹 氏 (東京大学大学院数理科学研究科)
Stallings-Swan’s Theorem for Borel graphs (JAPANESE)
[ 講演概要 ]
A Borel graph is a simplicial graph on a standard Borel space X such that the edge set is a Borel subset of X^2. Such objects have been studied in the context of countable Borel equivalence relations, and recently there are many attempts to apply the ideas of geometric group theory to them. Stallings-Swan's theorem states that groups of cohomological dimension 1 are free groups. We will talk about an analog of this theorem for Borel graphs: A Borel graph on X with uniformly bounded degrees of cohomological dimension 1 is Lipschitz equivalent to a Borel acyclic graph on X. This is proved by establishing a criterion for certain decomposition of Borel graphs, which is inspired by Dunwoody's work on accessibility of groups.
[ 参考URL ]A Borel graph is a simplicial graph on a standard Borel space X such that the edge set is a Borel subset of X^2. Such objects have been studied in the context of countable Borel equivalence relations, and recently there are many attempts to apply the ideas of geometric group theory to them. Stallings-Swan's theorem states that groups of cohomological dimension 1 are free groups. We will talk about an analog of this theorem for Borel graphs: A Borel graph on X with uniformly bounded degrees of cohomological dimension 1 is Lipschitz equivalent to a Borel acyclic graph on X. This is proved by establishing a criterion for certain decomposition of Borel graphs, which is inspired by Dunwoody's work on accessibility of groups.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
