Flat fully augmented links are determined by their complements
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912728165122048 |
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| author | Millichap, Christian Trapp, Rolland |
| author_facet | Millichap, Christian Trapp, Rolland |
| contents | In this paper, we show that two flat fully augmented links with homeomorphic complements must be equivalent as links in $\mathbb{S}^{3}$. This requires a careful analysis of how totally geodesic surfaces and cusps intersect in these link complements and behave under homeomorphism. One consequence of this analysis is a complete classification of flat fully augmented link complements that admit multiple reflection surfaces. In addition, our work classifies those symmetries of flat fully augmented link complements which are not induced by symmetries of the corresponding link. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02002 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Flat fully augmented links are determined by their complements Millichap, Christian Trapp, Rolland Geometric Topology 57K10, 57K32, 57M50 In this paper, we show that two flat fully augmented links with homeomorphic complements must be equivalent as links in $\mathbb{S}^{3}$. This requires a careful analysis of how totally geodesic surfaces and cusps intersect in these link complements and behave under homeomorphism. One consequence of this analysis is a complete classification of flat fully augmented link complements that admit multiple reflection surfaces. In addition, our work classifies those symmetries of flat fully augmented link complements which are not induced by symmetries of the corresponding link. |
| title | Flat fully augmented links are determined by their complements |
| topic | Geometric Topology 57K10, 57K32, 57M50 |
| url | https://arxiv.org/abs/2302.02002 |