## Geometry & Topology

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

#### Abstract

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

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

Dates
Revised: 6 October 2015
Accepted: 19 November 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510859088

Digital Object Identifier
doi:10.2140/gt.2016.20.3431

Mathematical Reviews number (MathSciNet)
MR3590355

Zentralblatt MATH identifier
06687798

#### Citation

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. https://projecteuclid.org/euclid.gt/1510859088

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