First topological-vertex computations of colored unknot and Hopf link invariants in RP^3 yield power series with positive integer q-expansions, conjecturally the Poincare series of a new link homology.
Torus Knots in Lens Spaces & Topological Strings
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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).
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Link in $\mathbb{R}\mathbb{P}^3$ and the Topological Vertex
First topological-vertex computations of colored unknot and Hopf link invariants in RP^3 yield power series with positive integer q-expansions, conjecturally the Poincare series of a new link homology.