## Algebraic & Geometric Topology

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

Hao Wu

#### 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.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715262

Digital Object Identifier
doi:10.2140/agt.2011.11.2037

Mathematical Reviews number (MathSciNet)
MR2826932

Zentralblatt MATH identifier
1232.57012

#### Citation

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. https://projecteuclid.org/euclid.agt/1513715262

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