Hyperbolicity of Links in Thickened Surfaces
| Autor: | Adams, Colin, Albors-Riera, Carlos, Haddock, Beatrix, Li, Zhiqi, Nishida, Daishiro, Wang, Braeden Reinoso. Luya |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Menasco showed that a non-split, prime, alternating link that is not a 2-braid is hyperbolic in $S^3$. We prove a similar result for links in closed thickened surfaces $S \times I$. We define a link to be fully alternating if it has an alternating projection from $S\times I$ to $S$ where the interior of every complementary region is an open disk. We show that a prime, fully alternating link in $S\times I$ is hyperbolic. Similar to Menasco, we also give an easy way to determine primeness in $S\times I$. A fully alternating link is prime in $S\times I$ if and only if it is "obviously prime". Furthermore, we extend our result to show that a prime link with fully alternating projection to an essential surface embedded in an orientable, hyperbolic 3-manifold has a hyperbolic complement. Comment: 17paghes, 18 figures |
| Databáze: | arXiv |
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