#### Volume 10, issue 1 (2010)

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

### Daniel Krasner

Algebraic & Geometric Topology 10 (2010) 1–32
##### 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 ${ℂℙ}^{n-1}$; 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 for $s{l}_{2}$–homology.

##### Keywords
link homology, categorification, quantum link invariants
Primary: 17B99
Secondary: 57M27
##### Publication
Received: 19 May 2008
Accepted: 30 September 2009
Published: 2 January 2010
##### Authors
 Daniel Krasner Department of Mathematics Columbia University 2990 Broadway New York NY 10027 USA http://math.columbia.edu/~dkrasner/