A Presentation For The Automorphisms Of The 3-Sphere That Preserve A Genus Two Heegaard Splitting

Erol Akbas

Published 2005-04-25, updated 2006-10-24Version 2

Scharlemann constructed a connected simplicial 2-complex $\Gamma$ with an action by the group ${\mathcal H_{2}}$ of isotopy classes of orientation preserving homeomorphisms of $S^3$ that preserve the isotopy class of an unknotted genus 2 handlebody $V$. In this paper we prove that the 2-complex $\Gamma$ is contractible. Therefore we get a finite presentation of ${\mathcal H_{2}}$.