Volume 8, issue 2 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M25
References
Publication
Received: 7 February 2008
Revised: 1 May 2008
Accepted: 2 May 2008
Published: 14 June 2008
Authors
Marc Lackenby
Mathematical Institute
University of Oxford
24-29 St Giles’
Oxford OX1 3LB
United Kingdom