  Scharlemann constructed a connected simplicial 2-complex $\Gamma$ 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
$\Gamma$ is contractible. Therefore we get a finite presentation of ${\mathcal
H_{2}}$.
