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

Erol Akbas

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

Erol Akbas

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Abstract

Scharlemann constructed a connected simplicial 2-complex $Γ$ 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 $Γ$ is contractible. Therefore we get a finite presentation of ${\mathcal H_{2}}$.

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Erol Akbas. 2006-10-24. A Presentation For The Automorphisms Of The 3-Sphere That Preserve A Genus Two Heegaard Splitting. https://arxiv.org/abs/math/0504519

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