Algebraic & Geometric Topology 1 (2001) 763–790

DOI: 10.2140/agt.2001.1.763

arXiv: math.GT/9811029

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, ie admits a Heegaard splitting obtained by attaching a single 1–handle to one or two components of ∂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

Mathematical Subject Classification

Primary: 57M99

References

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Publication

Received: 18 April 2001
Revised: 27 July 2001
Accepted: 3 October 2001
Published: 11 December 2001

Authors