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    Mathematics, Northeastern University, Boston

    Khovanov–Rozansky homology via a canopolis formalism

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    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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    Description

    Title : Khovanov–Rozansky homology via a canopolis formalism
    Author(s) : Ben Webster
    Abstract : 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.
    Subject : unspecified
    Area : Other
    Language : English
    Year : 2006

    Affiliations Mathematics, Northeastern University, Boston
    Journal : Algebraic & Geometric Topology
    Volume : 7
    Pages : 673 - 699
    Url : http://www.msp.warwick.ac.uk/agt/2007/07/p027.xhtml
    Doi : 10.2140/agt.2007.7.673

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