Mapping class group actions on configuration spaces and the Johnson filtration

Andrea Bianchi (University of Copenhagen)

Monday 8th November 16:00-17:00 Online

Abstract

This is joint work with Jeremy Miller and Jennifer Wilson. Let M be an orientable surface of genus g with one boundary curve, and let F_n(M) denote the configuration space of n ordered points in M. The action of Homeo(M,dM) on F_n(M) descends to an action of the mapping class group Gamma(M,dM) on the homology H_*(F_n(M)). Our main result is that, for all n,i>=0, the i-th stage J(i) of the Johnson’s filtration of Gamma(M,dM) acts trivially on H_i(F_n(M)). This extends previous work of Moriyama on certain relative configuration spaces.

I will recall the necessary definitions and give a sketch of the proof of the main theorem: the main inputs are Moriyama’s work and a cell stratification of F_n(M) à la Fox-Neuwirth-Fuchs. I will also present some examples of non-trivial actions of mapping classes in J(i-1) on elements of H_i(F_n(M)), for small values of i.

The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/98078798957 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).

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