The cohomological dimension of the hyperelliptic Torelli group

Geometry Topology Seminar
Monday, August 27, 2012 - 14:05
1 hour (actually 50 minutes)
Skiles 006
U Glasgow
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, for example in the context of the period mapping on the Torelli space of a Riemann surface and also 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 Leah Childers and Dan Margalit.