Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting

Abstract

An updated proof of a 1933 theorem of Goeritz, exhibiting a finite set of generators for the group of automorphisms of the 3-sphere that preserve a genus two Heegaard splitting. The group is analyzed via its action on a certain connected 2-complex. (The analogous problem for higher genus Heegaard splittings appears to remain unresolved.)

13 pages, 10 figures

Cited by in corpus (11)

• Primitive disk complexes for lens spaces
• Heegaard splittings of 3--manifolds (Haifa 2005): Problems
• Tunnel leveling, depth, and bridge numbers
• The depth of a knot tunnel
• Connected primitive disk complexes and genus two Goeritz groups of lens spaces
• Arc complexes, sphere complexes and Goeritz groups
• Convex-cocompact subgroups of the Goeritz group
• Homeomorphisms of the 3-sphere that preserve a Heegaard splitting of genus two
• Describing elements of the genus-2 Goeritz group of $S^3$
• The mapping class groups of reducible Heegaard splittings of genus two
• Constructing knot tunnels using giant steps