Derivation of the HOMFLYPT knot polynomial via helicity and geometric quantization

TL;DR

This paper offers a semiclassical interpretation of the HOMFLYPT knot polynomial by integrating hydrodynamical and symplectic geometric methods, providing new insights into knot invariants.

Contribution

It introduces a novel semiclassical framework connecting hydrodynamics and geometric quantization to derive the HOMFLYPT polynomial.

Findings

Establishes a link between hydrodynamical models and knot invariants.

Utilizes symplectic geometry to interpret framing in knot theory.

Provides a new perspective on the geometric quantization of knots.

Abstract

In this Letter we propose a semiclassical interpretation of the HOMFLYPT polynomial building on the Liu-Ricca hydrodynamical approach to the latter and on the Besana-S. symplectic approach to framing via Brylinski's manifold of mildly singular links.