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

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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 ${\mathcal H_{2}}$.
Completely rewritten. 21 pages with 22 figures

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Geometric Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/101228

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504519
 http://arxiv.org/abs/math/0504519

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arXiv