Mathematics

I will finish speaking on the topic from last week:
The embedding homogeneity group for a Cantor set C in S³ is the group of homeomorphisms of C that extend to homeomrophisms of S³ . 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.