Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
By Mikhail Khovanov, L. Rozansky. 2007
70 citations recorded by the source corpus.
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 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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a6827c3321985b5fc150ee09d156676de344dc6d
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Quantum (sln, ∧V n ) link invariant and matrix factorizations (2009, background): “Z-graded matrix factorization In this section, we recall definitions, properties and theorems given by [8][9][10][15][18][19][20].”