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

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

2005-04-25

arxiv.org/abs/math/0504519v2

Mathematics

Geometric Topology

Completely rewritten. 21 pages with 22 figures

Scientific paper

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 ${\mathcal H_{2}}$.

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