#### Volume 11, issue 4 (2011)

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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 $\mathfrak{s}\mathfrak{l}\left(N\right)$–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 $\mathfrak{s}\mathfrak{l}\left(N\right)$–homology. We also define and study colored $\mathfrak{s}\mathfrak{l}\left(N\right)$–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
Primary: 57M25
##### 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/