Invariants for Turaev genus one links
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866915447685775360 |
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| author | Dasbach, Oliver T. Lowrance, Adam M. |
| author_facet | Dasbach, Oliver T. Lowrance, Adam M. |
| contents | The Turaev genus defines a natural filtration on knots where Turaev genus zero knots are precisely the alternating knots. We show that the signature of a Turaev genus one knot is determined by the number of components in its all-A Kauffman state, the number of positive crossings, and its determinant. We also show that either the leading or trailing coefficient of the Jones polynomial of a Turaev genus one link (or an almost alternating link) has absolute value one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1604_03501 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Invariants for Turaev genus one links Dasbach, Oliver T. Lowrance, Adam M. Geometric Topology 57M25, 57M27 The Turaev genus defines a natural filtration on knots where Turaev genus zero knots are precisely the alternating knots. We show that the signature of a Turaev genus one knot is determined by the number of components in its all-A Kauffman state, the number of positive crossings, and its determinant. We also show that either the leading or trailing coefficient of the Jones polynomial of a Turaev genus one link (or an almost alternating link) has absolute value one. |
| title | Invariants for Turaev genus one links |
| topic | Geometric Topology 57M25, 57M27 |
| url | https://arxiv.org/abs/1604.03501 |