Equivariant 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(n)-equivariant cohomology ring of ${\mathbb{CP}}^{n-1}$; 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 in \cite{Kh3} for $s{l}_2$-homology.

28 pages, 23 figures