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Tuesday Seminar on Topology
Seminar information archive ～06/07｜Next seminar｜Future seminars 06/08～
| 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 |
2024/01/23
17:00-18:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Gefei Wang (The University of Tokyo)
On the rational cohomology of spin hyperelliptic mapping class groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Gefei Wang (The University of Tokyo)
On the rational cohomology of spin hyperelliptic mapping class groups (JAPANESE)
[ Abstract ]
Let G be the subgroup Sn−q×Sq of the n-th symmetric group Sn for n−q≥q. In this talk, we study the G-invariant part of the rational cohomology group of the pure braid group Pn. The invariant part H∗(Pn)G includes the rational cohomology of a spin hyperelliptic mapping class group of genus g as a subalgebra when n=2g+2. Based on the study of Lehrer-Solomon, we prove that they are independent of n and q in degree ∗≤q−1. We also give a formula to calculate the dimension of H∗(Pn)G and calculate it in all degree for q≤3.
[ Reference URL ]Let G be the subgroup Sn−q×Sq of the n-th symmetric group Sn for n−q≥q. In this talk, we study the G-invariant part of the rational cohomology group of the pure braid group Pn. The invariant part H∗(Pn)G includes the rational cohomology of a spin hyperelliptic mapping class group of genus g as a subalgebra when n=2g+2. Based on the study of Lehrer-Solomon, we prove that they are independent of n and q in degree ∗≤q−1. We also give a formula to calculate the dimension of H∗(Pn)G and calculate it in all degree for q≤3.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
