Mapping class groups of Heegaard splittings

Geometry & Topology
Event time: 
Thursday, February 1, 2007 - 11:30am to Wednesday, January 31, 2007 - 7:00pm
431 DL
Jesse Johnson
Speaker affiliation: 
Event description: 

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.