Computing closed essential surfaces in 3-manifolds
| Autor: | Burton, Benjamin A., Tillmann, Stephan |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | We present a practical algorithm to test whether a 3-manifold given by a triangulation or an ideal triangulation contains a closed essential surface. This property has important theoretical and algorithmic consequences. As a testament to its practicality, we run the algorithm over a comprehensive body of closed 3-manifolds and knot exteriors, yielding results that were not previously known. The algorithm derives from the original Jaco-Oertel framework, involves both enumeration and optimisation procedures, and combines several techniques from normal surface theory. Our methods are relevant for other difficult computational problems in 3-manifold theory, such as the recognition problem for knots, links and 3-manifolds. Comment: 25 pages, 15 figures; journal version of the conference paper arXiv:1212.1531 |
| Databáze: | arXiv |
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