### The cohomological dimension of the hyperelliptic Torelli group

- Series
- Geometry Topology Seminar
- Time
- Monday, August 27, 2012 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Tara Brendle – 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.