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 |
Abstract |
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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Pages | 116-214 |
Download |
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Submitted: | January 23, 2007 |
Revised: | November 23, 2007 |
Accepted: | November 24, 2007 |
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