Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
Abstract
We suggest a categorification procedure for the SO(2N) onevariable specialization of the twovariable Kauffman polynomial. The construction has many similarities with the HOMFLYPT 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 Z_2 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 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2007
 DOI:
 10.48550/arXiv.math/0701333
 arXiv:
 arXiv:math/0701333
 Bibcode:
 2007math......1333K
 Keywords:

 Mathematics  Quantum Algebra;
 18G60