Flop Invariance of Refined Topological Vertex and Link Homologies

Abstract

It has been proposed recently that the topological A-model string theory on local toric Calabi-Yau manifolds has a two parameter extension. Amplitudes of the two parameter topological strings can be computed using a diagrammatic method called the refined topological vertex. In this paper we study properties of the refined amplitudes under the flop transition of toric Calabi-Yau three-folds. We also discuss that the slicing invariance and the flop transition imply a simple formula for the homological sl(N) invariants of the Hopf link. The new expression for the invariants gives a simple refinement of the Hopf link invariant of Chern-Simons theory.