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Clasp technology to knot homology via the affine Grassmannian

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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 Cautis and Kamnitzer (Duke Math J 142:511–588, 2008; Invent Math 174:165–232, 2008) from standard to arbitrary representations.

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Acknowledgments

I would like to thank Pramod Achar, Joel Kamnitzer, Mikhail Khovanov, Aaron Lauda, Anthony Licata, Jacob Rasmussen, Raphael Rouquier, Lev Rozansky, Noah Snyder and Joshua Sussan for helpful discussions. Lauda and Rasmussen also corrected and helped with the calculations in Sect. 10. Research was supported by NSF grant DMS-1101439 and the Alfred P. Sloan foundation.

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  1. Department of Mathematics, University of British Columbia, Vancouver, Canada

    Sabin Cautis

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Cautis, S. Clasp technology to knot homology via the affine Grassmannian. Math. Ann. 363, 1053–1115 (2015). https://doi.org/10.1007/s00208-015-1196-x

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