  One of the distinctive features of hole-doped cuprate superconductors is the
onset of a `pseudogap' below a temperature $T^*$. Recent experiments suggest
that there may be a connection between the existence of the pseudogap and the
topology of the Fermi surface. Here, we address this issue by studying the
two-dimensional Hubbard model with two distinct numerical methods. We find that
the pseudogap only exists when the Fermi surface is hole-like and that, for a
broad range of parameters, its opening is concomitant with a Fermi surface
topology change from electron- to hole-like. We identify a common link between
these observations: the pole-like feature of the electronic self-energy
associated with the formation of the pseudogap is found to also control the
degree of particle-hole asymmetry, and hence the Fermi surface topology
transition. We interpret our results in the framework of an SU(2) gauge theory
of fluctuating antiferromagnetism. We show that a mean-field treatment of this
theory in a metallic state with U(1) topological order provides an explanation
of this pole-like feature, and a good description of our numerical results. We
discuss the relevance of our results to experiments on cuprates.
