Event Type:

Topology Seminar

Date/Time:

Monday, September 24, 2012 - 05:00

Location:

GILK 113

Local Speaker:

Abstract:

The *embedding homogeneity group* for a Cantor set C in S^{3} is the group of homeomorphisms of C that extend to homeomrophisms of S^{3} . The groups ranges from the full set of homeomorphisms of C (if C is standardly embedded) to only the identity homeopmorphism (if C is rigidly embedded). We show that for each finitely generated abelian group G there is an embedded Cantor set C_{G} with embedding homogeneity group G. This has implications for the mapping class group of the three-manifold complement of C.