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Linear Analysis on singular spaces
L^2-de Rham-Hodge and L^2-Atiyah-Bott-Lefschetz Theorems on stratified pseudomanifolds
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During the last 30 years stratified pseudomanifolds turned out to be a very reach field of interactions between analysis and topology. The aim of this book is to explore some of these interactions. More precisely the book is divided in two parts. The first half is dedicated to the relationships between the L^2 de Rham cohomology, Hodge cohomology (both associated to a suitable incomplete riemannian metric) and the intersection cohomology of a stratified pseudomanifold. In particular the question of the Poincaré duality for the L^2 cohomology associated to an incomplete metric is discussed. The second half concerns the generalization of the well known theorem of Atiyah-Bott for elliptic complexes over a closed manifolds to the case of elliptic complexes of cone differential operators over a manifold with conical singularities.
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