#### Volume 1, issue 2 (2001)

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

### Eric Sedgwick

Algebraic & Geometric Topology 1 (2001) 763–790
 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 $\partial {M}_{i}$. This result also holds for a decomposition of $M$ along a maximal collection of incompressible tori.

##### Keywords
3–manifold, Heegaard splitting, incompressible surface
Primary: 57M99
##### Publication
Received: 18 April 2001
Revised: 27 July 2001
Accepted: 3 October 2001
Published: 11 December 2001
##### Authors
 Eric Sedgwick DePaul University Department of Computer Science 243 S Wabash Ave Chicago IL 60604 USA