Alexander and writhe polynomials for virtual knots

Abstract

We give a new interpretation of the Alexander polynomial ${\Delta }_0$ for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, ${\Delta }_0$ 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.

22 pages, 19 figures

References in corpus (1)

• On Alexander-Conway Polynomials for Virtual Knots and Links