  This paper establishes an isomorphism between the Bar-Natan skein module of
the solid torus with a particular boundary curve system and the homology of the
(n,n) Springer variety. The results build on Khovanov's work with crossingless
matchings and the cohomology of the (n,n) Springer variety. We also give a
formula for comultiplication in the Bar-Natan skein module for this specific
three-manifold and boundary curve system.
