Homology, Homotopy and Applications

Volume 12 (2010)

Number 2

Rouquier complexes are functorial over braid cobordisms

Pages: 109 – 146

DOI: https://dx.doi.org/10.4310/HHA.2010.v12.n2.a4

Authors

Ben Elias (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Dan Krasner (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)

Abstract

Using the diagrammatic calculus for Soergel bimodules developed by B. Elias and M. Khovanov, we show that Rouquier complexes are functorial over braid cobordisms. We explicitly describe the chain maps which correspond to movie move generators.

Keywords

Soergel bimodule, Rouquier complex, link homology, braid cobordism

2010 Mathematics Subject Classification

20F36, 57M27

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Published 1 January 2010