Algebraic & Geometric Topology

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

Hao Wu

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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.

Article information

Algebr. Geom. Topol., Volume 11, Number 4 (2011), 2037-2106.

Received: 11 November 2010
Revised: 17 May 2011
Accepted: 17 May 2011
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

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


Wu, Hao. Generic deformations of the colored $\mathfrak{sl}(N)$–homology for links. Algebr. Geom. Topol. 11 (2011), no. 4, 2037--2106. doi:10.2140/agt.2011.11.2037.

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