An infinite torus braid yields a categorified Jones-Wenzl projector

By L. Rozansky. 2010

77 citations recorded by the source corpus.

A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e03c97d4aac17f582ce2316854e48269919f730f

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Functoriality of colored link homologies (2017, background): “In the other approach, the invariants for other colors are computed by inserting infinite twists into fundamentally colored cables of the original link, see Rozansky [48] for the case of N = 2 and Cautis [10] for the general case.”
Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols (2012, background): “Independently, to the present work, such categorifications were defined and studied in [17] and [53].”
Categorification of the Jones-Wenzl Projectors (2010, background): “We would like to add that more recently Lev Rozansky [Roz10] has proposed an elegant idea on categorification of the Jones-Wenzl projectors, based on the properties of the infinite torus braid.”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “Using the foamation 2-functor ΦCMW , the above procedure also gives a construction of the categorified Jones-Wenzl projectors from [22] and [63] in the CMW foam setting.”
Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology (2016, background): “Shende ([32]), the first and the third authors gave a precise conjectural description of the stable glN homology of (n,∞) torus knots, which is known ([15, 36, 50, 51]) to be isomorphic to the glN homology of the categorified projector P(1,.”