Homeomorphisms of the 3-sphere that preserve a Heegaard splitting of genus two

Cho, Sangbum

doi:10.1090/S0002-9939-07-09188-5

Homeomorphisms of the 3-sphere that preserve a Heegaard splitting of genus two
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Proc. Amer. Math. Soc. 136 (2008), 1113-1123 Request permission

Abstract:

Let ${\mathcal H_2}$ be the group of isotopy classes of orientation-preserving homeomorphisms of $\mathbb S^3$ that preserve a Heegaard splitting of genus two. In this paper, we construct a tree in the barycentric subdivision of the disk complex of a handlebody of the splitting to obtain a finite presentation of ${\mathcal H_2}$.

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