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

DOI: 10.2140/pjm.2008.236.201

Abstract

Scharlemann constructed a connected simplicial 2-complex Γ with an action by the group ℋ₂ 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 ℋ₂.

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