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An
algorithm to determine the Heegaard genus of simple
$3$–manifolds with nonempty boundary
Marc Lackenby |
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Algebraic & Geometric Topology 8 (2008) 911–934
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Abstract |
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We provide an algorithm to determine the Heegaard genus of simple –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. |
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Keywords
Heegaard, algorithm, 3-manifold
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Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M25
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References |
Publication
Received: 7 February 2008
Revised: 1 May 2008
Accepted: 2 May 2008
Published: 14 June 2008
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Authors |
| Marc Lackenby | |
| Mathematical Institute University of Oxford 24-29 St Giles’ Oxford OX1 3LB United Kingdom |
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