THE GENUS TWO GOERITZ GROUP OF S-2 x S-1

Abstract

The genus-g Goeritz group is the group of isotopy classes of orientationpreserving 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 x S-1 is finitely presented, and give its explicit presentation.