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Tuesday Seminar on Topology
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2023/04/11
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kazuo Habiro (The Univesity of Tokyo)
On the stable cohomology of the (IA-)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.
Kazuo Habiro (The Univesity of Tokyo)
On the stable cohomology of the (IA-)automorphism groups of free groups (JAPANESE)
[ Abstract ]
By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.
[ Reference URL ]By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
