Geometry, Topology and Dynamics Seminar
Nathan Broaddus
University of 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.
Monday March 9, 2009 at 3:00 PM in SEO 612