Year: 2026
Type: preprint
Abstract: We introduce a generalization of the Jones polynomial for classical and virtual knots and links using colorings by a permutation $σ:X\to X$ of a finite set $X$. For $X=\{1\}$ and for classical knots, the invariant is equivalent to the usual Jones polynomial; for $X$ with cardinality greater than 1 the invariant expresses distinct information from the Jones polynomial or virtual knots and for classical and virtual links. We establish some properties of the new invariants and compute the polynomials for classical and virtual knots and links of small crossing number for a few small permutations.
Source: arXiv (Cornell University)
Author: Nelson, Sam
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167270748
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