  The topology of the Fermi surface of an extended $d-p$ Hubbard model is
investigated using the Green's function technique in a n-pole approximation.
The effects of the $d-p$ hybridization on the Fermi surface are the main focus
in the present work. Nevertheless, the effects of doping, Coulomb interaction
and hopping to second-nearest-neighbors on the Fermi surface, are also studied.
Particularly, it is shown that the crossover from hole-like to electron-like
Fermi surface (Lifshitz transition) is deeply affected by the $d-p$
hybridization. Moreover, the pseudogap present in the low doping regime is also
affected by the hybridization. The results show that both the doping and the
hybridization act in the sense of suppresses the pseudogap. Therefore, the
systematic investigation of the Fermi surface topology, shows that not only the
doping but also the hybridization can be considered as a control parameter for
both the pseudogap and the Lifshitz transition. Assuming that the hybridization
is sensitive to external pressure, the present results agree qualitatively with
recent experimental data for the cuprate Nd-LSCO.
