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Genus two 3-manifolds are built from handle number one pieces

Eric Sedgwick
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Abstract

Let M be a closed, irreducible, genus two 3-manifold, and F a maximal collection of pairwise disjoint, closed, orientable, incompressible surfaces embedded in M. Then each component manifold M_i of M-F has handle number at most one, i.e. admits a Heegaard splitting obtained by attaching a single 1-handle to one or two components of boundary M_i. This result also holds for a decomposition of M along a maximal collection of incompressible tori.

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Eric Sedgwick. 2001-12-31. Genus two 3-manifolds are built from handle number one pieces. https://doi.org/10.2140/agt.2001.1.763

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