Vol. 236, No. 2, 2008

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ISSN: 0030-8730
A presentation for the automorphisms of the 3-sphere that preserve a genus two Heegaard splitting

Erol Akbas

Vol. 236 (2008), No. 2, 201–222
Abstract

Scharlemann constructed a connected simplicial 2-complex Γ with an action by the group 2 of isotopy classes of orientation-preserving homeomorphisms of S3 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 2.

Keywords
Heegaard, genus two handlebody, three-sphere
Mathematical Subject Classification 2000
Primary: 57M60
Secondary: 57M20
Milestones
Received: 19 October 2006
Revised: 13 February 2008
Accepted: 19 February 2008
Published: 1 June 2008
Authors
Erol Akbas
Georgia State University
Department of Mathematics and Statistics
30 Pryor Street
Atlanta, GA 30303
United States