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

摘要

Scharlemann constructed a connected simplicial 2-complex Gamma with an action by the group 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 H-2.