On the determinant of checkerboard colorable virtual knots
Volume 273 / 2026
Fundamenta Mathematicae 273 (2026), 47-61
MSC: Primary 57K12; Secondary 57K10, 57K16
DOI: 10.4064/fm240809-4-1
Published online: 29 January 2026
Abstract
For classical knots, Murasugi showed that the determinant modulo $8$ is classified by the Arf invariant. Boden and Karimi introduced a determinant for checkerboard colorable virtual knots. We prove that this determinant modulo $8$ is classified by the coefficient of $z^2$ in the ascending polynomial, an extension of the Conway polynomial for classical knots.
