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

Download
COinS