On the complexity of 2-bridge link complements
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917937967792128 |
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| author | Morgan, James Spreer, Jonathan |
| author_facet | Morgan, James Spreer, Jonathan |
| contents | We reprove a necessary condition for the Sakuma-Weeks triangulation of a 2-bridge link complement to be minimal in terms of the mapping class describing its alternating 4-string braid construction. For the 2-bridge links satisfying this condition we construct explicit angle structures on the Sakuma-Weeks triangulations and compute both multiplicative and additive lower bounds on the complexity of the link complements via volume estimates. These lower bounds are an improvement on existing volume estimates for the 2-bridge links examined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09629 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the complexity of 2-bridge link complements Morgan, James Spreer, Jonathan Geometric Topology 57Q15, 57K31, 57K32, 57K10 We reprove a necessary condition for the Sakuma-Weeks triangulation of a 2-bridge link complement to be minimal in terms of the mapping class describing its alternating 4-string braid construction. For the 2-bridge links satisfying this condition we construct explicit angle structures on the Sakuma-Weeks triangulations and compute both multiplicative and additive lower bounds on the complexity of the link complements via volume estimates. These lower bounds are an improvement on existing volume estimates for the 2-bridge links examined. |
| title | On the complexity of 2-bridge link complements |
| topic | Geometric Topology 57Q15, 57K31, 57K32, 57K10 |
| url | https://arxiv.org/abs/2406.09629 |