  We provide the first complete computations of colored sl(N) homology for a
nontrivial knot. In doing so, we show that the colored sl(N) homology of the
trefoil labeled by an exterior power of the defining representation is
isomorphic to the cohomology of a closed manifold naturally associated to the
trefoil. This manifold is the set of homomorphisms from the fundamental group
of the complement of the trefoil to SU(N) that send meridians to a particular
conjugacy class depending on the label. We also provide complete computations
and analogous isomorphisms for the first nontrivial link, the Hopf link.
