Volume 11, issue 4 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Generic deformations of the colored $\mathfrak{sl}(N)$–homology for links

Hao Wu

Algebraic & Geometric Topology 11 (2011) 2037–2106
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 sl(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 sl(N)–homology. We also define and study colored sl(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/