2014/05/11 by Matt Hogancamp, Hogancamp, Matt · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1405.2574
openalex publication_date 2014/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct an action of a polynomial ring on the colored sl(2) link homology of Cooper-Krushkal, over which this homology is finitely generated. We define a new, related link homology which is finite dimensional, extends to tangles, and categorifies a scalar-multiple of the sl(2) Reshetikhin-Turaev invariant. We expect this homology to be functorial under 4-dimensional cobordisms. The polynomial action is related to a conjecture of Gorsky-Oblomkov-Rasmussen-Shende on the stable Khovanov homology of torus knots, and as an application we obtain a weak version of this conjecture. A key new ingredient is the construction of a bounded chain complex which categorifies a scalar multiple of the Jones-Wenzl projector, in which the denominators have been cleared.