The critical temperature T c in the universal phase diagram of cuprate superconductors is a function of two variables: the hole-doping δ and a material dependent parameter. Here we focus on the behavior of T c,max as a function of the material dependent parameter (MDP) at the optimum hole doping. We have discussed the correlation between (1) the average Cu----O (planar) distance, or the strain of the Cu----O bond, (2) the nearest-neighbor hopping t and (3) the Lifshitz parameter z. These Lifshitz parameter z = µ δ = 0.16 −E vHs which are all material dependent parameters, where µ δ = 0.16 is the chemical potential at optimum doping and E vHs is the energy of the Van Hove singularity, defines the proximity to the Fermi surface topological transition from electron-like to hole-like. The results show that the striped phases occur for z < 0, the highest T c,max for z ≈ 55 meV and the drop of T c,max for z > 75 meV.