The Steinberg module and level structures for surfaces with marked points

Tara Brendle (University of Glasgow)

Monday 21st October 16:00-17:00 Maths 311B

Abstract

It is known by work of Harer and Ivanov that the mapping class group of a surface is a virtual duality group, and that its dualizing module is the Steinberg module, that is, the unique nonzero homology group of the complex of curves associated to the surface. In this talk, we will describe the Steinberg module for surfaces with marked points and explain applications to finding nontrivial cohomology in the level L congruence subgroups of the corresponding mapping class groups. This is work in progress with Andy Putman and Nathan Broaddus; it builds on work of Fullarton-Putman in the case of closed surfaces. 

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