Equivariant $\mathit{sl}(n)$–link homology

Abstract

For every positive integer $n$ we construct a bigraded homology theory for links, such that the corresponding invariant of the unknot is closely related to the $U\left(n\right)$–equivariant cohomology ring of ${ℂ\mathbb{P}}^{n-1}$; our construction specializes to the Khovanov–Rozansky $s{l}_n$–homology. We are motivated by the “universal” rank two Frobenius extension studied by M Khovanov for $s{l}_2$–homology.