Torus Knots in Lens Spaces & Topological Strings

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).

31 pages, 2 figures; v2: section 2 rewritten, other minor changes

References in corpus (6)

• Open string amplitudes and large order behavior in topological string theory
• Torus knots and mirror symmetry
• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots
• Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions
• Introduction to the Gopakumar-Vafa Large N Duality
• Legendrian torus knots in lens spaces

Cited by in corpus (2)

• Distinguishing Mutant Knots
• Equivalence of two diagram representations of links in lens spaces and essential invariants