The action of full twist on the superpolynomial for torus knots

TL;DR

This paper extends Kálmán's full twist formula from the HOMFLY polynomial to superpolynomials for positive toric braids, utilizing Mellit's recent results to generalize the known invariants.

Contribution

It introduces a generalized formula for superpolynomials of positive toric braids based on the full twist, expanding the understanding of knot invariants.

Findings

Generalization of the full twist formula to superpolynomials

Application of Mellit's recent results to knot invariants

Enhanced computational framework for torus knot invariants

Abstract

We show, using Mellit's recent results, that K\'alm\'an's full twist formula for the HOMFLY polynomial can be generalized to a formula for superpolynomials in the case of positive toric braids.