Published in Journal of Gökova Geometry Topology, Volume 1 (2007)
Title Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
Author Mikhail Khovanov and Lev Rozansky
We suggest a categorification procedure for the SO(2N) one-variable specialization of the two-variable Kauffman polynomial. The construction has many similarities with the HOMFLY-PT categorification: a planar graph formula for the polynomial is converted into a complex of graded vector spaces, each of them being the homology of a Z2-graded differential vector space associated to a graph and constructed using matrix factorizations. This time, however, the elementary matrix factorizations are not Koszul; instead, they are convolutions of of chain complexes of Koszul matrix factorizations.
We prove that the homotopy class of the resulting complex associated to a diagram of a link is invariant under the first two Reidemeister moves and conjecture its invariance under the third move.
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Submitted: January 23, 2007
Revised: November 23, 2007
Accepted: November 24, 2007
 Journal of GGT Volume 1

Last updated: December 2007
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