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For every positive integer $n$ we construct a bigraded homology theory forlinks, such that the corresponding invariant of the unknot is closely relatedto the U(n)-equivariant cohomology ring of $\mathbb{CP}^{n-1}$; ourconstruction specializes to the Khovanov-Rozansky $sl_n$-homology. We aremotivated by the "universal" rank two Frobenius extension studied by M.Khovanov in \cite{Kh3} for $sl_2$-homology.

Equivariant sl(n)-link homology