An algorithm to determine the Heegaard genus of simple 3–manifolds with nonempty boundary

Lackenby, Marc

doi:10.2140/agt.2008.8.911

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An algorithm to determine the Heegaard genus of simple $3$–manifolds with nonempty boundary

Marc Lackenby

Algebraic & Geometric Topology 8 (2008) 911–934

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.

Keywords

Heegaard, algorithm, 3-manifold

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M25

References

Publication

Received: 7 February 2008

Revised: 1 May 2008

Accepted: 2 May 2008

Published: 14 June 2008

Authors

Marc Lackenby
Mathematical Institute University of Oxford 24-29 St Giles’ Oxford OX1 3LB United Kingdom

Volume 8, issue 2 (2008)