Symmetric homology for surfaces
Tara Brendle (University of Glasgow)
Monday 24th May, 2010 16:00-17:00 Mathematics Building, room 204
The hyperelliptic (or symmetric) Torelli group of a surface S is the subgroup of the mapping class group of S consisting of elements which commute with a fixed hyperelliptic involution of S and which also act trivially on the first homology of S. We will describe an approach to a conjecture of Hain regarding the generation of this group which leads to a "symmetric homology" theory for surfaces. In particular, we give symmetric analogues of certain classical results characterizing the relationship between the algebraic structure of H_1(S) and geometric representations of its elements. This is joint work with Dan Margalit of Tufts University.