Torus Knots in Lens Spaces & Topological Strings

TL;DR

This paper explores quantum invariants of knots in lens spaces, generalizes known formulas for torus knots, and proposes a topological string theory model to describe these knots.

Contribution

It extends the Rosso-Jones formula to torus knots in lens spaces and introduces a B-model topological string theory framework for these knots.

Findings

Derived a generalized Rosso-Jones formula for torus knots in L(p,1)

Proposed a B-model topological string theory description for torus knots in L(2,1)

Established connections between quantum invariants and topological strings in lens spaces

Abstract

We study the invariant of knots in lens spaces defined from quantum Chern-Simons theory. By means of the knot operator formalism, we derive a generalization of the Rosso-Jones formula for torus knots in L(p,1). In the second part of the paper, we propose a B-model topological string theory description of torus knots in L(2,1).