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We review and apply Cheeger-Gromov theory on $l^2$-cohomology of infinitecoverings of complete manifolds with bounded curvature and finite volume.Applications focus on $l^2$-cohomology of (pullback of) harmonic Higgs bundleson some covering of Zariski open sets of K\"ahler manifolds. The$l^2-$Dolbeault to DeRham spectral sequence of these Higgs bundles is seen todegenerate at $E_2$.

Application of Cheeger-Gromov theory to the $l^2$-cohomology of harmonic Higgs bundles over covering of finite volume complete manifolds