The band structures of pure and hole doped La_2CuO_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

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... 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 the cuprates.