Algebraic & Geometric Topology

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

Hao Wu

Full-text: Open access

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

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

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

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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