English

CWR sequence of invariants of alternating links and its properties

Geometric Topology 2025-05-27 v3 Combinatorics

Abstract

We present the CWRCWR invariant, a new invariant for alternating links, which builds upon and generalizes the WRPWRP invariant. The CWRCWR invariant is an array of two-variable polynomials that provides a stronger invariant compared to the WRPWRP invariant. We compare the strength of our invariant with the classical HOMFLYPT, Kauffman 33-variable, and Kauffman 22-variable polynomials on specific knot examples. Additionally, we derive general recursive "skein" relations, and also specific formulas for the initial components of the CWRCWR invariant using weighted adjacency matrices of modified Tait graphs.

Keywords

Cite

@article{arxiv.2406.04987,
  title  = {CWR sequence of invariants of alternating links and its properties},
  author = {Michal Jablonowski},
  journal= {arXiv preprint arXiv:2406.04987},
  year   = {2025}
}