Midwest Topology Seminar
Northwestern University
May 3, 2008
- Nathan Broaddus (Chicago)
Homology of the curve complex and the Steinberg module of the mapping class
group
Abstract:
The homology of the curve complex is of fundamental importance for the
homology of the mapping class group. It was previously known to be an
infinitely generated free abelian group, but to date, its structure as a
mapping class group module has gone unexplored. I will give a resolution
for the homology of the curve complex as a mapping class group module. From
the presentation coming from the last two terms of this resolution I will
show that this module is cyclic and give an explicit single generator. As a
corollary, this generator is a homologically nontrivial sphere in the curve
complex.