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