Scharlemann constructed a connected simplicial 2-complex Ξ with an
action by the group H2β 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
Ξ is contractible. Therefore we get a finite presentation of H2β.Comment: Completely rewritten. 21 pages with 22 figure