#### Volume 8, issue 2 (2008)

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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
##### 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
Primary: 57N10
Secondary: 57M25