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

الأصل · EN

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.