## Tuesday Seminar on Topology

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) KOHNO Toshitake, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya Tea: 16:30 - 17:00 Common Room

### 2022/11/15

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Arthur Soulié (IBS Center for Geometry and Physics, POSTECH)
Stable cohomology of mapping class groups with some particular twisted contravariant coefficients (ENGLISH)
[ Abstract ]
The twisted cohomology of mapping class groups of compact orientable surfaces (with one boundary) is very difficult to compute generally speaking. In this talk, I will describe the computation of the stable cohomology algebra of these mapping class groups with twisted coefficients given by the first homology of the unit tangent bundle of the surface. This type of computation is out of the scope of the traditional framework for homological stability. Indeed, these twisted coefficients define a contravariant functor over the classical category associated to mapping class groups to study homological stability, rather than a covariant one. I will also present the computation of the stable cohomology algebras with with twisted coefficients given by the exterior powers and tensor powers of the first homology of the unit tangent bundle of the surface. All this represents a joint work with Nariya Kawazumi.
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html