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We consider a generalized Hubbard model with on-site and nearest-neighbour repulsions U and V respectively, and nearest-neighbour hopping far spin up (down) which depends on the total occupation n(b) of spin down (up) electrons on both sites involved. The hopping parameters are t(AA), t(AB) and t(BB) for n(b) = 0, 1, 2 respectively. We briefly summarize results which support that the model exhibits s-wave superconductivity for certain parameters and extend them by studying the Berry phases. Using a generalized Hartree-Fock(HF) BCS decoupling of the two and three-body terms, we obtain that at half filling, for t(AB) < t(AA) = t(BB) and sufficiently small U and V the model leads to triplet p-wave superconductivity for a simple cubic lattice in any dimension. In one dimension, the resulting phase diagram is compared with that obtained numerically using two quantized Berry phases (topological numbers) as order parameters. While this novel method supports the previous results, there are quantitative differences

Superconductivity with s and p symmetries in an extended Hubbard model with correlated hopping