Genus Two 3–manifolds Are Built from Handle Number One Pieces
نویسنده
چکیده
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 Mi of M − F has handle number one, i.e. admits a Heegaard splitting obtained by attaching a single 1–handle to one or two components of ∂Mi. This result also holds for a decomposition of M along a maximal collection of incompressible tori.
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