Clasp technology to knot homology via the affine Grassmannian
Sabin Cautis
TL;DR
This paper develops a categorification of Reshetikhin-Turaev tangle invariants of type A using affine Grassmannian techniques, extending previous work to arbitrary representations through a new approach involving clasps as infinite twists.
Contribution
It introduces a novel categorification of clasps as infinite twists and extends the categorification of tangle invariants to all representations in type A.
Findings
Categorification of all Reshetikhin-Turaev tangle invariants of type A.
Introduction of clasps as infinite twists for categorification.
Extension of previous work to arbitrary representations using affine Grassmannian varieties.
Abstract
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 Kamnitzer from standard to arbitrary representations.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology