Invariants for Turaev genus one links

Oliver T. Dasbach; Adam M. Lowrance

doi:10.4310/cag.2018.v26.n5.a4

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arXiv · 1604.03501

Invariants for Turaev genus one links

Oliver T. Dasbach·Adam M. Lowrance

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Abstract

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.

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BibTeX RIS

Oliver T. Dasbach, Adam M. Lowrance. 2016-04-12. Invariants for Turaev genus one links. https://doi.org/10.4310/cag.2018.v26.n5.a4

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