The genus two Goeritz group of $S^2\times S^1$

Abstract

The genus-g Goeritz group is the group of isotopy classes of orientation-preserving homeomorphisms of a closed orientable 3-manifold that preserve a given genus-g Heegaard splitting of the manifold. In this work, we show that the genus-2 Goeritz group of $S^2\times S^1$ is finitely presented, and give its explicit presentation.

minor changes; to appear in Mathematical Research Letters

References in corpus (2)

• Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting
• Primitive disk complexes for lens spaces

Cited by in corpus (3)

• Arc complexes, sphere complexes and Goeritz groups
• Disk complexes and genus two Heegaard splittings for non-prime 3-manifolds
• A twisted first homology group of the Goeritz group of 3-sphere