Georgia Institute of Technology College of Sciences

We will prove that the mapping class group is finitely presented, using its action on the arc complex. We will also use the curve complex to show that the abstract commensurator of the mapping class group is the extended mapping class group. If time allows, we will introduce the complex of minimizing cycles for a surface, and use it to compute the cohomological dimension of the Torelli subgroup of the mapping class group. This is a followup to the previous talk, but will be logically independent.