General perversities and \(L^2\) de Rham and Hodge theorems for stratified pseudomanifolds

DOI10.1016/j.bulsci.2013.10.001zbMath1283.55002arXiv1107.3972OpenAlexW2963136731MaRDI QIDQ2637618

Francesco Bei

Publication date: 13 February 2014

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3972

zbMATH Keywords

intersection cohomology\(L^2\)-cohomologystratified pseudomanifoldHodge cohomologygeneral perversity

Mathematics Subject Classification ID

de Rham theory in global analysis (58A12) Hodge theory in global analysis (58A14) Stratified sets (58A35) Intersection homology and cohomology in algebraic topology (55N33)

Related Items (9)

Signatures of Witt spaces with boundary ⋮ \(L^2\)-harmonic forms on incomplete Riemannian manifolds with positive Ricci curvature ⋮ The \(L^2\)-Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities: a heat kernel approach ⋮ Poincaré duality, Hilbert complexes and geometric applications ⋮ Comparison between two complexes on a singular space ⋮ Sobolev spaces and Bochner Laplacian on complex projective varieties and stratified pseudomanifolds ⋮ \(q\)-parabolicity of stratified pseudomanifolds and other singular spaces ⋮ On the L2-Poincaré duality for incomplete Riemannian manifolds: A general construction with applications ⋮ On the eigenforms of compact stratified spaces

Cites Work

• Intersection homology with general perversities
• Intersection homology. II
• \(L^ 2\)-cohomology and intersection homology of stratified spaces
• Intersection cohomology. (Notes of a Seminar on Intersection Homology at the University of Bern, Switzerland, Spring 1983)
• Topological invariance of intersection homology without sheaves
• Intersection homology theory
• Hilbert complexes
• \(\mathcal L^ 2\)-cohomologie des espaces stratifiés. (\(\mathcal L^ 2\)- cohomology of stratified spaces)
• \(L^ p\) cohomology of cones and horns
• Hodge and signature theorems for a family of manifolds with fibre bundle boundary
• Harmonic fields in Riemannian manifolds (Generalized potential theory)
• The signature package on Witt spaces
• Singular chain intersection homology for traditional and super-perversities
• On the spectral geometry of spaces with cone-like singularities
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