Year: 2024
Type: article
Abstract: We present the [Formula: see text] invariant, a new invariant for alternating links, which builds upon and generalizes the [Formula: see text] invariant. The [Formula: see text] invariant is an array of two-variable polynomials that provides a stronger invariant compared to the [Formula: see text] invariant. We compare the strength of our invariant with the classical HOMFLYPT, Kauffman [Formula: see text]-variable, and Kauffman [Formula: see text]-variable polynomials on specific knot examples. Additionally, we derive general recursive “skein” relations, and also specific formulas for the initial components of the [Formula: see text] invariant using weighted adjacency matrices of modified Tait graphs.
Author: Michał Jabłonowski
Institution: University of Gdańsk
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404183875