Describing elements of the genus-2 Goeritz group of $S^3$

Abstract

In this article we present a finite generating set $G_2$ of ${\mathcal{H}}_2$, the genus-2 Goeritz group of $S^3$, in terms of Dehn twists about certain simple closed curves on the standard Heegaard surface. We present an algorithm that describes an element $\psi \in {\mathcal{H}}_2$ as a word in the alphabet of $G_2$ in a certain format. Using a complexity measure defined on reducing spheres, we show that such a description of $\psi$ is unique.

References in corpus (1)

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