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2008 An algorithm to determine the Heegaard genus of simple $3$–manifolds with nonempty boundary
Marc Lackenby
Algebr. Geom. Topol. 8(2): 911-934 (2008). DOI: 10.2140/agt.2008.8.911

Abstract

We provide an algorithm to determine the Heegaard genus of simple 3–manifolds with nonempty boundary. More generally, we supply an algorithm to determine (up to ambient isotopy) all the Heegaard splittings of any given genus for the manifold. As a consequence, the tunnel number of a hyperbolic link is algorithmically computable. Our techniques rely on Rubinstein’s work on almost normal surfaces, and also on a new structure called a partially flat angled ideal triangulation.

Citation

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Marc Lackenby. "An algorithm to determine the Heegaard genus of simple $3$–manifolds with nonempty boundary." Algebr. Geom. Topol. 8 (2) 911 - 934, 2008. https://doi.org/10.2140/agt.2008.8.911

Information

Received: 7 February 2008; Revised: 1 May 2008; Accepted: 2 May 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1154.57018
MathSciNet: MR2443101
Digital Object Identifier: 10.2140/agt.2008.8.911

Subjects:
Primary: 57N10
Secondary: 57M25

Rights: Copyright © 2008 Mathematical Sciences Publishers

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Vol.8 • No. 2 • 2008
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