Factors of HOMFLY polynomials
Douglas Blackwell, Damiano Testa
TL;DR
This paper investigates the factorization properties of HOMFLY polynomials for knots and links, providing computational analysis and an irreducibility criterion related to graph theory.
Contribution
It introduces a new irreducibility criterion for HOMFLY polynomials linked to 2-connected plane graphs and reports computational findings on knots with up to 12 crossings.
Findings
Identified 17 non-trivial factorizations in knots with up to 12 crossings.
Developed an irreducibility criterion for HOMFLY polynomials of certain links.
Provided computational evidence supporting the criterion.
Abstract
We study factorizations of HOMFLY polynomials of certain knots and oriented links. We begin with a computer analysis of knots with at most 12 crossings, finding 17 non-trivial factorizations. Next, we give an irreducibility criterion for HOMFLY polynomials of oriented links associated to 2-connected plane graphs.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · graph theory and CDMA systems