L^p-cohomology, heat semigroup and stratified spaces

2020/12/14 by Francesco Bei, Bei, Francesco
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2012.07684

Abstract

Let (M,g) be an incomplete Riemannian manifold of finite volume and let 2≤ p<∞. In the first part of this paper we prove that under certain assumptions the inclusion of the space of L^p-differential forms into that of L²-differential forms gives rise to an injective/surjective map between the corresponding L^p and L² cohomology groups. Then in the second part we provide various applications of these results to the curvature and the intersection cohomology of compact Thom-Mather stratified pseudomanifolds and complex projective varieties with only isolated singularities.

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