Volume 20, issue 6 (2016)

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

David E V Rose and Paul Wedrich

Geometry & Topology 20 (2016) 3431–3517

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.

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categorification, link homology, spectral sequence
Mathematical Subject Classification 2010
Primary: 17B37, 57M25, 81R50
Received: 10 May 2015
Revised: 6 October 2015
Accepted: 19 November 2015
Published: 21 December 2016
Proposed: Ciprian Manolescu
Seconded: Tomasz Mrowka, Ronald Stern
David E V Rose
University of North Carolina at Chapel Hill
Mathematics Department
120 E Cameron Avenue
CB #3250
329 Phillips Hall
Chapel Hill, NC 27599
United States
Paul Wedrich
Department of Mathematics
Imperial College London
United Kingdom