English

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

Geometric Topology 2016-01-20 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0709.0376,
  title  = {An algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary},
  author = {Marc Lackenby},
  journal= {arXiv preprint arXiv:0709.0376},
  year   = {2016}
}

Comments

23 pages, 14 figures