Computing closed essential surfaces in 3-manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2018
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| _version_ | 1866911028308082688 |
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| author | Burton, Benjamin A. Tillmann, Stephan |
| author_facet | Burton, Benjamin A. Tillmann, Stephan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_11686 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Computing closed essential surfaces in 3-manifolds Burton, Benjamin A. Tillmann, Stephan Geometric Topology 57M25, 57N10 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. |
| title | Computing closed essential surfaces in 3-manifolds |
| topic | Geometric Topology 57M25, 57N10 |
| url | https://arxiv.org/abs/1812.11686 |