On the determinant of checkerboard colorable virtual knots
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 z2 in the ascending polynomial, an extension of the Conway polynomial for classical knots.
Fields of Study & Subjects
3D Shape Modeling and Analysis
Computational Geometry and Mesh Generation
Computer Graphics and Visualization Techniques
Publication details
- Journal / source
- Fundamenta Mathematicae
- Publication date
- 29 January 2026
- Language
- EN