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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Weber-Seifert dodecahedral space is non-Haken


Authors: Benjamin A. Burton, J. Hyam Rubinstein and Stephan Tillmann
Journal: Trans. Amer. Math. Soc. 364 (2012), 911-932
MSC (2010): Primary 57N10
Published electronically: October 5, 2011
MathSciNet review: 2846358
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Abstract: In this paper we settle Thurston's old question of whether the Weber-Seifert dodecahedral space is non-Haken, a problem that has been a benchmark for progress in computational 3-manifold topology over recent decades. We resolve this question by combining recent significant advances in normal surface enumeration, new heuristic pruning techniques, and a new theoretical test that extends the seminal work of Jaco and Oertel.


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Additional Information

Benjamin A. Burton
Affiliation: School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072, Australia
Email: bab@maths.uq.edu.au

J. Hyam Rubinstein
Affiliation: Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia
Email: rubin@ms.unimelb.edu.au

Stephan Tillmann
Affiliation: School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072, Australia
Email: tillmann@maths.uq.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05419-X
PII: S 0002-9947(2011)05419-X
Keywords: Haken manifold, Weber-Seifert dodecahedral space, normal surface, incompressible surface
Received by editor(s): March 3, 2010
Received by editor(s) in revised form: July 10, 2010
Published electronically: October 5, 2011
Additional Notes: The first author was supported under the Australian Research Council’s Discovery funding scheme (project DP1094516).
The second and third authors were partially supported under the Australian Research Council’s Discovery funding scheme (projects DP0664276 and DP1095760).
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.