TOPOLOGY SEMINAR

2/8/2007

Jesse Johnson
Yale University

Mapping class groups of Heegaard splittings

The mapping class group of a Heegaard splitting is the group of automorphisms of the ambient manifold that take the Heegaard surface onto itself.  There is a canonical homomorphism from this group into the mapping class group of the 3-manifold.  I will outline a proof that for high distance Heegaard splittings this homomorphism is an isomorphism, then describe examples of low distance, irreducible Heegaard for which the kernel is infinite.