  The band structures of pure and hole doped La$_2$CuO$_4$ with
antiferromagnetic (AFM) spin-fluctuations are calculated and compared to
spectral weights of ARPES. It is shown that observations of coexisting Fermi
surface (FS) arcs and closed FS pockets are consistent with modulated AFM spin
fluctuations of varying wave lengths. Large variations of strong spin
fluctuations make the outer part of the FS break diffuse at low doping. This
part of the FS is suppressed at high doping when spin fluctuations are weak.
The resulting superimposed spectral weight has features both from FS arcs and
closed pockets. A connection between results of ARPES, neutron scattering, and
band results for the modulated AFM spin wave state, suggests that spin-phonon
coupling is an important mechanism for the %pseudogap and other properties of
the cuprates.
