Extremal Khovanov homology of Turaev genus one links
| Autor: | Dasbach, Oliver T., Lowrance, Adam M. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Fundamenta Mathematicae 250 (2020), 63-99 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4064/fm729-9-2019 |
| Popis: | The Turaev genus of a link can be thought of as a way of measuring how non-alternating a link is. A link is Turaev genus zero if and only if it is alternating, and in this viewpoint, links with large Turaev genus are very non-alternating. In this paper, we study Turaev genus one links, a class of links which includes almost alternating links. We prove that the Khovanov homology of a Turaev genus one link is isomorphic to $\mathbb{Z}$ in at least one of its extremal quantum gradings. As an application, we compute or nearly compute the maximal Thurston Bennequin number of a Turaev genus one link. Comment: 30 pages, 18 figures |
| Databáze: | arXiv |
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