Volume 7, issue 2 (2007)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Khovanov–Rozansky homology via a canopolis formalism

Ben Webster

Algebraic & Geometric Topology 7 (2007) 673–699

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