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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 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.

Keywords
3–manifold, Heegaard splitting, incompressible surface
Mathematical Subject Classification 2000
Primary: 57M99
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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