  We establish a direct map between refined topological vertex and sl(N)
homological invariants of the of Hopf link, which include Khovanov-Rozansky
homology as a special case. This relation provides an exact answer for
homological invariants of the of Hopf link, whose components are colored by
arbitrary representations of sl(N). At present, the mathematical formulation of
such homological invariants is available only for the fundamental
representation (the Khovanov-Rozansky theory) and the relation with the refined
topological vertex should be useful for categorifying quantum group invariants
associated with other representations (R_1, R_2). Our result is a first direct
verification of a series of conjectures which identifies link homologies with
the Hilbert space of BPS states in the presence of branes, where the physical
interpretation of gradings is in terms of charges of the branes ending on
Lagrangian branes.
