Title

Invariants for turaev genus one links

Document Type

Article

Publication Date

1-1-2018

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 Kaufiman state, the number of positive crossings, and its determinant. We also show that either the leading or trailing coeficient of the Jones polynomial of a Turaev genus one link (or an almost alternating link) has absolute value one.

Publication Source (Journal or Book title)

Communications in Analysis and Geometry

First Page

1103

Last Page

1126

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