Algebraic & Geometric Topology

Khovanov–Rozansky homology via a canopolis formalism

Ben Webster

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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.

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 673-699.

Dates
Received: 23 February 2007
Accepted: 5 March 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796701

Digital Object Identifier
doi:10.2140/agt.2007.7.673

Mathematical Reviews number (MathSciNet)
MR2308960

Zentralblatt MATH identifier
1135.57007

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 13D02: Syzygies, resolutions, complexes

Keywords
Khovanov–Rozansky homology knot homology canopolis planar algebra

Citation

Webster, Ben. Khovanov–Rozansky homology via a canopolis formalism. Algebr. Geom. Topol. 7 (2007), no. 2, 673--699. doi:10.2140/agt.2007.7.673. https://projecteuclid.org/euclid.agt/1513796701


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References

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