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 manifold with bounded curvature and finite volume. Applications focus on l 2 −cohomology of (pullback of) harmonic Higgs bundles on coverings of Zariski open sets of Kähler manifolds. The l 2 −Hodge to DeRham spectral sequence of these Higgs bundles is seen to degenerate at E 2 .

Towards a L 2 cohomology theory for Hodge modules on infinite covering spaces: L 2 constructible cohomology and L 2 de Rham cohomology for coherent D-modules

“…The recent preprint [18] suggests an extension of the theory for twistor D Xmodules might be possible.…”