Geodesic
Genus two 3–manifolds are built from handle number one pieces
Sedgwick, Eric1
1DePaul University, Department of Computer Science, 243 S Wabash Ave, Chicago IL 60604, USA
Algebraic and Geometric Topology, Tome 1 (2001) no. 2, pp. 763-790
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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 at most one, ie 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.

DOI : 10.2140/agt.2001.1.763
Keywords: 3–manifold, Heegaard splitting, incompressible surface

Sedgwick, Eric  1

1 DePaul University, Department of Computer Science, 243 S Wabash Ave, Chicago IL 60604, USA 
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Sedgwick, Eric. Genus two 3–manifolds are built from handle number one pieces. Algebraic and Geometric Topology, Tome 1 (2001) no. 2, pp. 763-790. doi: 10.2140/agt.2001.1.763

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