Homology of the curve complex and the Steinberg module of the mapping class group

Thursday, October 7, 2010 -
4:30pm to 6:30pm
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.
Speaker: 
Nathan Broaddus
Ohio State University
Event Location: 
Fine Hall 314