2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101228Scharlemann constructed a connected simplicial 2-complex $Γ$ with an action by the group ${\mathcal H_{2}}$ 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 $Γ$ is contractible. Therefore we get a finite presentation of ${\mathcal H_{2}}$.Completely rewritten. 21 pages with 22 figuresGeometric Topologytext