We use foams to give a topological construction of a rational link homology
categorifying the slN link invariant, for N>3. To evaluate closed foams we use
the Kapustin-Li formula adapted to foams by Khovanov and Rozansky. We show that
for any link our homology is isomorphic to Khovanov and Rozansky's.Comment: The Kapustin-Li formula has been corrected for facets with non-zero
genus and its normalization and some signs have been changed accordingly. 43
pages, lots of figure