Robust implications on Dark Matter from the first FERMI sky gamma map

We derive robust model-independent bounds on DM annihilations and decays from the first year of FERMI gamma-ray observations of the whole sky. These bounds only have a mild dependence on the DM density profile and allow the following DM interpretations of the PAMELA and FERMI electron/positron excesses: primary channels mu+ mu-, mu+ mu-mu+mu- or e+ e- e+ e-. An isothermal-like density profile is needed for annihilating DM. In all such cases, FERMI gamma spectra must contain a significant DM component, that may be probed in the future.Comment: 16 pages, 8 figures. Final versio