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

Abstract

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 ${\mathcal{H}}_2$.

Completely rewritten. 21 pages with 22 figures

Cited by in corpus (1)

• Automorphisms of the three-torus preserving a genus three Heegaard splitting