Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
| dc.creator | Khovanov, Mikhail | |
| dc.creator | Rozansky, Lev | |
| dc.date | 2007-01-12 | |
| dc.date.accessioned | 2026-07-07T07:40:36Z | |
| dc.date.available | 2026-07-07T07:40:36Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0701333 | |
| dc.identifier | http://arxiv.org/abs/math/0701333 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121822 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 18G60 | |
| dc.title | Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial | |
| dc.type | text |