Knot homology and sheaves on the Hilbert scheme of points on the plane

For each braid beta is an element of Br-n we construct a 2-periodic complex S-beta of quasicoherent C* x C*-equivariant sheaves on the non-commutative nested Hilbert scheme Hilb(1,n)(free) . We show that the triply graded vector space of the hypercohomology H(S-beta circle times boolean AND center dot(B)) with B being tautological vector bundle, is an isotopy invariant of the knot obtained by the closure of beta. We also show that the support of cohomology of the complex S-beta is supported on the ordinary nested Hilbert scheme Hilb(1,n). Hilb(1,n)(free) , that allows us to relate the triply graded knot homology to the sheaves on Hilb(1,n).