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トポロジー火曜セミナー
過去の記録 ～03/19｜次回の予定｜今後の予定 03/20～
| 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 |
2024年10月29日(火)
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/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。
内藤 貴仁 氏 (日本工業大学)
Cartan calculus in string topology (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。
内藤 貴仁 氏 (日本工業大学)
Cartan calculus in string topology (JAPANESE)
[ 講演概要 ]
The homology of the free loop space of a closed oriented manifold (called the loop homology) has rich algebraic structures. In the theory of string topology due to Chas and Sullivan, it is well known that the loop homology has a structure of Gerstenhabar algebras with a multiplication called the loop product and a Lie bracket called the loop bracket. On the other hand, Kuribayashi, Wakatsuki, Yamaguchi and the speaker gave a Cartan calculus on the loop homology, which is a geometric description of a homotopy Cartan calculus in the sense of Fiorenza and Kowalzig on the Hochschild homology.
In this talk, we will investigate a relationship between the string topology operations and the Cartan calculus. Especially, we will show that the Cartan calculus can be described by using the loop product and the loop bracket with rational coefficients. As an application, the nilpotency of some loop homology classes are determined.
[ 参考URL ]The homology of the free loop space of a closed oriented manifold (called the loop homology) has rich algebraic structures. In the theory of string topology due to Chas and Sullivan, it is well known that the loop homology has a structure of Gerstenhabar algebras with a multiplication called the loop product and a Lie bracket called the loop bracket. On the other hand, Kuribayashi, Wakatsuki, Yamaguchi and the speaker gave a Cartan calculus on the loop homology, which is a geometric description of a homotopy Cartan calculus in the sense of Fiorenza and Kowalzig on the Hochschild homology.
In this talk, we will investigate a relationship between the string topology operations and the Cartan calculus. Especially, we will show that the Cartan calculus can be described by using the loop product and the loop bracket with rational coefficients. As an application, the nilpotency of some loop homology classes are determined.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
