Application of Cheeger-Gromov theory to the l²-cohomology of harmonic Higgs bundles over covering of finite volume complete manifolds

2018/10/09 by Pascal Dingoyan, Dingoyan, Pascal, Georg Schumacher +1
Mathematics · #32L10 #58A14 #Algebraic Geometry and Number Theory #Bounded function #Cohomology #Combinatorics #Complex Variables (math.CV) #Curvature #De Rham cohomology #Degenerate energy levels #Equivariant cohomology #FOS: Mathematics #Finite volume method #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Harmonic #Higgs boson #Mathematical analysis #Mathematics #Particle physics #Physics #Pullback #Pure mathematics #Spectral sequence #Topology (electrical circuits) #math.CV #msc:32L10 #msc:58A14

paper · pdf · doi:10.48550/arxiv.1810.03863

published in arXiv (Cornell University) (Cornell University)

arxiv created 2018/10/09 · openalex publication_date 2018/10/09 · arxiv updated 2018/10/10 · openalex created_date 2018/10/26 · openalex updated_date 2026/07/28

Abstract

We review and apply Cheeger-Gromov theory on l²-cohomology of infinite coverings of complete manifolds with bounded curvature and finite volume. Applications focus on l²-cohomology of (pullback of) harmonic Higgs bundles on some covering of Zariski open sets of Kähler manifolds. The l²-Dolbeault to DeRham spectral sequence of these Higgs bundles is seen to degenerate at E₂.

Citations

• The Self-Duality Equations on a Riemann Surface
• On the parabolic kernel of the Schrödinger operator
• On the heat equation and the index theorem
• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules

Related

• Vanishing theorem for tame harmonic bundles via L²-cohomology
• Cohomologies of unipotent harmonic bundles over quasi-projective varieties I: The case of noncompact curves
• Direct Images in Non Abelian Hodge Theory
• Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles
• Hodge structure on the cohomology of the moduli space of Higgs bundles