Khovanov–Rozansky homology via a canopolis formalism

Webster, Ben

doi:10.2140/agt.2007.7.673

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Khovanov–Rozansky homology via a canopolis formalism

Ben Webster

Algebraic & Geometric Topology 7 (2007) 673–699

DOI: 10.2140/agt.2007.7.673

arXiv: math.GT/0610650

Abstract

In this paper, we describe a canopolis (ie categorified planar algebra) formalism for Khovanov and Rozansky’s link homology theory. We show how this allows us to organize simplifications in the matrix factorizations appearing in their theory. In particular, it will put the equivalence of the original definition of Khovanov–Rozansky homology and the definition using Soergel bimodules in a more general context, allow us to give a new proof of the invariance of triply graded homology and give a new analysis of the behavior of triply graded homology under the Reidemeister IIb move.

Keywords

Khovanov–Rozansky homology, knot homology, canopolis, planar algebra

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 13D02

References

Publication

Received: 23 February 2007

Accepted: 5 March 2007

Published: 10 May 2007

Authors

Ben Webster
Department of Mathematics University of California Berkeley, CA 94720
http://math.berkeley.edu/~bwebste

Volume 7, issue 2 (2007)