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Tuesday Seminar on Topology
Seminar information archive ～05/23｜Next seminar｜Future seminars 05/24～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | HABIRO Kazuo, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2025/01/21
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Ryotaro Kosuge (The University of Tokyo)
Rational abelianizations of Chillingworth subgroups of mapping class groups and automorphism groups of free groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Ryotaro Kosuge (The University of Tokyo)
Rational abelianizations of Chillingworth subgroups of mapping class groups and automorphism groups of free groups (JAPANESE)
[ Abstract ]
The Chillingworth subgroup of the mapping class group of a surface is defined as the subgroup consisting of elements that preserve nonsingular vector fields up to homotopy. The action of the mapping class group on the set of homotopy classes of nonsingular vector fields is described using the concept of the winding number. By employing a cohomological approach, we extend the notion of the winding number to general manifolds, introducing the definition of the Chillingworth subgroup for both the mapping class group of general manifolds and the automorphism group of a free group. In this work, we determine the rational abelianization of the Chillingworth subgroup of the mapping class group of a surface and, under a certain assumption, also determine the rational abelianization of the Chillingworth subgroup for the automorphism group of a free group.
[ Reference URL ]The Chillingworth subgroup of the mapping class group of a surface is defined as the subgroup consisting of elements that preserve nonsingular vector fields up to homotopy. The action of the mapping class group on the set of homotopy classes of nonsingular vector fields is described using the concept of the winding number. By employing a cohomological approach, we extend the notion of the winding number to general manifolds, introducing the definition of the Chillingworth subgroup for both the mapping class group of general manifolds and the automorphism group of a free group. In this work, we determine the rational abelianization of the Chillingworth subgroup of the mapping class group of a surface and, under a certain assumption, also determine the rational abelianization of the Chillingworth subgroup for the automorphism group of a free group.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
