Geometry & Topology

Deformations of colored $\mathfrak{sl}_{N}$ link homologies via foams

David Rose and Paul Wedrich

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We prove a conjectured decomposition of deformed slN link homology, as well as an extension to the case of colored links, generalizing results of Lee, Gornik, and Wu. To this end, we use foam technology to give a completely combinatorial construction of Wu’s deformed colored slN link homologies. By studying the underlying deformed higher representation-theoretic structures and generalizing the Karoubi envelope approach of Bar-Natan and Morrison, we explicitly compute the deformed invariants in terms of undeformed type A link homologies of lower rank and color.

Article information

Geom. Topol., Volume 20, Number 6 (2016), 3431-3517.

Received: 10 May 2015
Revised: 6 October 2015
Accepted: 19 November 2015
First available in Project Euclid: 16 November 2017

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Zentralblatt MATH identifier

Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37]

categorification link homology spectral sequence


Rose, David; Wedrich, Paul. Deformations of colored $\mathfrak{sl}_{N}$ link homologies via foams. Geom. Topol. 20 (2016), no. 6, 3431--3517. doi:10.2140/gt.2016.20.3431.

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