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2001 Genus two 3–manifolds are built from handle number one pieces
Eric Sedgwick
Algebr. Geom. Topol. 1(2): 763-790 (2001). DOI: 10.2140/agt.2001.1.763

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 MF 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.

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Eric Sedgwick. "Genus two 3–manifolds are built from handle number one pieces." Algebr. Geom. Topol. 1 (2) 763 - 790, 2001. https://doi.org/10.2140/agt.2001.1.763

Information

Received: 18 April 2001; Revised: 27 July 2001; Accepted: 3 October 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0977.57015
MathSciNet: MR1875617
Digital Object Identifier: 10.2140/agt.2001.1.763

Subjects:
Primary: 57M99

Rights: Copyright © 2001 Mathematical Sciences Publishers

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