  We generalize the works of Lee [arXiv:math/0210213v3] and Gornik
[arXiv:math/0402266v2] to construct a basis for generic deformations of the
colored sl(N)-homology defined in [arXiv:1002.2662v1]. As applications, we
construct non-degenerate pairings and co-pairings which lead to dualities of
generic deformations of the colored sl(N)-homology. We also define and study
colored sl(N)-Rasmussen invariants. Among other things, we observe that these
invariants vanish on amphicheiral knots and discuss some implications of this
observation.
