Invariants for Turaev genus one links
Geometric Topology
2025-08-19 v2
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.
Cite
@article{arxiv.1604.03501,
title = {Invariants for Turaev genus one links},
author = {Oliver T. Dasbach and Adam M. Lowrance},
journal= {arXiv preprint arXiv:1604.03501},
year = {2025}
}
Comments
17 pages, 13 figures. Theorem 1.3 in version 1 is now Equation 3.2 in version 2. To appear in Communications in Analysis and Geometry