TG-Hyperbolicity of Composition of Virtual Knots
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917881569083392 |
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| author | Adams, Colin Simons, Alexander |
| author_facet | Adams, Colin Simons, Alexander |
| contents | The composition of any two nontrivial classical knots is a satellite knot, and thus, by work of Thurston, is not hyperbolic. In this paper, we explore the composition of virtual knots, which are an extension of classical knots that generalize the idea of knots in $S^3$ to knots in $S \times I$ where $S$ is a closed orientable surface. We prove that for any two hyperbolic virtual knots, there is a composition that is hyperbolic. We then obtain strong lower bounds on the volume of the composition using information from the original knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_09859 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | TG-Hyperbolicity of Composition of Virtual Knots Adams, Colin Simons, Alexander Geometric Topology 57K12, 57K32 The composition of any two nontrivial classical knots is a satellite knot, and thus, by work of Thurston, is not hyperbolic. In this paper, we explore the composition of virtual knots, which are an extension of classical knots that generalize the idea of knots in $S^3$ to knots in $S \times I$ where $S$ is a closed orientable surface. We prove that for any two hyperbolic virtual knots, there is a composition that is hyperbolic. We then obtain strong lower bounds on the volume of the composition using information from the original knots. |
| title | TG-Hyperbolicity of Composition of Virtual Knots |
| topic | Geometric Topology 57K12, 57K32 |
| url | https://arxiv.org/abs/2110.09859 |