USA Topology Seminar

Generic properties in the mapping class group

Joseph Maher, CUNY College of Staten Island

Details
Friday, September 3, 2010  
  ILB 370
  3:30-4:30 pm  

Abstract The mapping class group is the group of all homeomorphisms from a surface to itself, up to isotopy. It occurs naturally whenever you glue surfaces together, for example in the theory of 3-manifolds, the monodromy maps of fiber bundles over S1, and the gluing maps for Heegaard splittings, are both given by elements of the mapping class group.

What properties does a "typical" element of the mapping class group have? We discuss some different notions of "typical", and apply methods from geometric group theory to identify some of their properties. We will mention some applications to 3-manifolds.