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

Wu, Hao¹

¹Department of Mathematics, The George Washington University, Monroe Hall, Room 240, 2115 G Street, NW, Washington DC 20052, USA

Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 2037-2106

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.2037

Classification : 57M25
Keywords: Khovanov–Rozansky homology, matrix factorization, symmetric polynomial, Rasmussen invariant, amphicheiral knot

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