An algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary

Details An algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary An algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary

2007-09-04

arxiv.org/abs/0709.0376v2

Mathematics

Geometric Topology

23 pages, 14 figures

Scientific paper

We provide an algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty 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 a new structure called a partially flat angled ideal triangulation.

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