Alexander and writhe polynomials for virtual knots

Authors

Blake Mellor, Loyola Marymount UniversityFollow

Document Type

Article - post-print

Publication Date

2016

Abstract

We give a new interpretation of the Alexander polynomial Δ₀ for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, Δ₀ determines the writhe polynomial of Cheng and Gao (equivalently, Kauffman's affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.

Comments

This is a post-print version of the article.

Recommended Citation

Mellor, B., 2016: Alexander and writhe polynomials for virtual knots. J. Knot Theory Ramif., 25.8, arXiv:1601.07153.