Cohomology of the hyperelliptic Torelli group

Tara Brendle (University of Glasgow)

Monday 16th January, 2012 15:00-16:00 416


The hyperelliptic Torelli group SI(S) is the subgroup of the mapping class group of a surface S consisting of elements which commute with a fixed hyperelliptic involution and which act trivially on homology. The group SI(S) appears in a variety of settings, including in the context of the period mapping on the Torelli space of a Riemann surface and as a kernel of the classical Burau representation of the braid group. We will show that the cohomological dimension of SI(S) is g -1; this result fits nicely into a pattern with other subgroups of the mapping class group, particularly those of the Johnson filtration. This is joint work with Childers and Margalit.

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