General perversities and L² de Rham and Hodge theorems for stratified pseudomanifolds

2011/07/20 by Francesco Bei, Bei, Francesco · 1 citation
Mathematics · #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1107.3972

openalex publication_date 2011/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a compact stratified pseudomanifold with a Thom-Mather stratification and a class of riemannian metrics over its regular part, we study the relationships between the L² de Rham and Hodge cohomology and the intersection cohomology of X associated to some perversities. More precisely, to a kind of metric which we call quasi edge with weights, we associate two general perversities in the sense of G. Friedman, p_g and its dual q_g. We then show that the absolute L² Hodge cohomology is isomorphic to the maximal L² de Rham cohomology and this is in turn isomorphic to the intersection cohomology associated to the perversity q_g. Moreover we prove that the relative L² Hodge cohomology is isomorphic to the minimal L² de Rham cohomology and this is in turn isomorphic to the intersection cohomology associated to the perversity p_g.

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

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