Generic deformations of the colored sl(N)–homology for links

Wu, Hao

doi:10.2140/agt.2011.11.2037

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Generic deformations of the colored $\mathfrak{sl}(N)$–homology for links

Hao Wu

Algebraic & Geometric Topology 11 (2011) 2037–2106

DOI: 10.2140/agt.2011.11.2037

Abstract

We generalize the works of Lee [Adv. Math. 197 (2005) 554–586] and Gornik [arXiv math.QA/0402266] to construct a basis for generic deformations of the colored $s l (N)$ –homology defined in [arXiv 1002.2662v2]. As applications, we construct nondegenerate pairings and co-pairings which lead to dualities of generic deformations of the colored $s l (N)$ –homology. We also define and study colored $s l (N)$ –Rasmussen invariants. Among other things, we observe that these invariants vanish on amphicheiral knots and discuss some implications of this observation.

Keywords

Khovanov–Rozansky homology, matrix factorization, symmetric polynomial, Rasmussen invariant, amphicheiral knot

Mathematical Subject Classification 2010

Primary: 57M25

References

Publication

Received: 11 November 2010

Revised: 17 May 2011

Accepted: 17 May 2011

Published: 22 July 2011

Authors

Hao Wu
Department of Mathematics The George Washington University Monroe Hall, Room 240 2115 G Street, NW Washington DC 20052 USA
http://home.gwu.edu/~haowu/

Volume 11, issue 4 (2011)