Clasp technology to knot homology via the affine Grassmannian

By Sabin Cautis. 2012

85 citations recorded by the source corpus.

We categorify all the Reshetikhin–Turaev tangle invariants of type A. Our main tool is a categorification of the generalized Jones–Wenzl projectors (a.k.a. clasps) as infinite twists. Applying this to certain convolution product varieties on the affine Grassmannian we extend our earlier work with Cautis and Kamnitzer (Duke Math J 142:511–588, 2008; Invent Math 174:165–232, 2008) from standard to arbitrary representations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f5162f76cab19a29ab28367ee16f67836e593856

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

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,.”
Deformations of colored sl(N) link homologies via foams (2015, background): “Moreover, similarly to the case discussed in [QR], any link homologies defined using the images of the Rickard complexes in a “skew Howe” 2-representation factoring through Ǔ0≤NQ (glm) Σ must agree (see the work of Cautis [Cau2] for the first appearance of this idea).”
Light ladders and clasp conjectures (2015, background): “25b) κ(b,c,d),(1010) = [2] − 1 κ(b,c−1,d),(1010) .”
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.”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “In [9], Cautis showed that given any categorification of the skew Howe representations ∧N q (C n q ⊗C m q ), one obtains a categorification of sln clasps, the sln analogs of the Jones-Wenzl projectors, using the higher representation theory of the categorified quantum group.”
The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality (2014, methodology): “Indeed, Cautis presents6 the Rickard complexes in this context [4].”