Algebraic and Geometric Topology 1 (2001), paper no. 38, pages 763-790.

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

Eric Sedgwick

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.

Keywords. 3-manifold, Heegaard splitting, incompressible surface

AMS subject classification. Primary: 57M99.

DOI: 10.2140/agt.2001.1.763

E-print: arXiv:math.GT/9811029

Submitted: 18 April 2001. (Revised: 27 July 2001.) Accepted: 3 October 2001. Published: 11 December 2001.

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Eric Sedgwick
DePaul University, Department of Computer Science
243 S Wabash Ave, Chicago, IL 60604, USA

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