The Weber-Seifert dodecahedral space is non-Haken
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- by Benjamin A. Burton, J. Hyam Rubinstein and Stephan Tillmann PDF
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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.References
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Additional Information
- Benjamin A. Burton
- Affiliation: School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072, Australia
- MR Author ID: 739103
- Email: bab@maths.uq.edu.au
- J. Hyam Rubinstein
- Affiliation: Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia
- MR Author ID: 151465
- Email: rubin@ms.unimelb.edu.au
- Stephan Tillmann
- Affiliation: School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072, Australia
- MR Author ID: 663011
- ORCID: 0000-0001-6731-0327
- Email: tillmann@maths.uq.edu.au
- 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). - © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 911-932
- MSC (2010): Primary 57N10
- DOI: https://doi.org/10.1090/S0002-9947-2011-05419-X
- MathSciNet review: 2846358