Bar-Natan homology for null-homologous links in RP^3 and genus bound

We will define a Bar-Natan homology for null homologous links in RP^3. As in the case for the usual Bar-Natan homology, this gives rise to a s-invariant and certain genus bound for null homologous knots in RP^3. More explicitly, it gives a genus bound for equivariant slice surface bounding the lift of the knot in S^3, such that the involution reverses the orientation on the surface.