Equivariant sl(n)-link homology

Krasner, Daniel

doi:10.2140/agt.2010.10.1

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

Daniel Krasner

Algebraic & Geometric Topology 10 (2010) 1–32

DOI: 10.2140/agt.2010.10.1

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 ${ℂ ℙ}^{n - 1}$ ; 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.

Keywords

link homology, categorification, quantum link invariants

Mathematical Subject Classification 2000

Primary: 17B99

Secondary: 57M27

References

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/

Volume 10, issue 1 (2010)