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

Abstract

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