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

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.
Publication status:
Published

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Publisher copy:
10.2140/agt.2008.8.911

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
ALGEBRAIC AND GEOMETRIC TOPOLOGY
Volume:
8
Issue:
2
Pages:
911-934
Publication date:
2007-09-04
DOI:
EISSN:
1472-2739
ISSN:
1472-2739
URN:
uuid:fe73f590-8282-40d0-bd2f-eb4bb9aa4586
Source identifiers:
15983
Local pid:
pubs:15983
Language:
English
Keywords:

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