2016•arXiv (Cornell University)Open access

Polynomial Invariants of Torus Knots and (p,q)-Calculus

A.M. Pavlyuk

Abstract

We introduce the deformed fermionic numbers, corresponding to the skein relations, the main characteristics of knots and links. These fermionic numbers allow one to restore the skein relations. For the Alexander (Jones) skein relation we introduce corresponding Alexander (Jones) fermionic q-numbers, and for the HOMFLY skein relation - the HOMFLY deformed (p,q)-numbers with one fermionic parameter.

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Key concepts: Torus, Mathematics, Alexander polynomial, Pure mathematics, Polynomial, Combinatorics, Calculus (dental), Algebra over a field