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Abstract
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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.
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Keywords
Khovanov–Rozansky homology, knot homology, canopolis,
planar algebra
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Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 13D02
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Publication
Received: 23 February 2007
Accepted: 5 March 2007
Published: 10 May 2007
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