Mathematics – Geometric Topology
Scientific paper
2006-10-23
Algebraic and Geometric Topology 7 (2007), 673-699
Mathematics
Geometric Topology
24 pages, 7 figures. v3: edited introduction and fixed diagram 1, plus minor changes
Scientific paper
10.2140/agt.2007.7.673
In this paper, we describe a canopolis (i.e. 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 new analysis of the behavior of triply graded homology under the Reidemeister IIb move.
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