On the cohomology of L²-harmonic forms of an incomplete Riemannian manifold

2025/12/15 by Francesco Bei, Bei, Francesco, Mauro Spreafico +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2512.13854

openalex publication_date 2025/12/15 · openalex created_date 2025/12/18 · openalex updated_date 2026/07/28

Abstract

Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric applications of our construction to incomplete Riemannian manifolds with particular interest to the case of smoothly stratified Thom-Mather spaces.

Citations

• The signature package on Witt spaces
• General perversities and L² de Rham and Hodge theorems for stratified pseudomanifolds
• Cohomology of Harmonic Forms on Riemannian Manifolds With Boundary

Related

• Cohomology of Harmonic Forms on Riemannian Manifolds With Boundary
• L^p-cohomology, heat semigroup and stratified spaces
• L² cohomology of Manifolds with flat ends
• Harmonic forms on manifolds with edges
• On the L²-Poincaré duality for incomplete riemannian manifolds: a general construction with applications