Von Neumann invariants of coherent analytic sheaves
type: Item
instance of: scholarly article
title: Von Neumann invariants of coherent analytic sheaves
zbMATH Open document ID: 0964.32008
DOI: 10.1007/PL00004413
author: Philippe Eyssidieux
published in: Mathematische Annalen
publication date: 2000-11-27T00:00:00Z
review text: Let \(Y\to X\) be a Galois covering of complex analytic spaces with Galois group \(G\) and \(X\) compact. Here the author constructs a theory of \(L^p\)-cohomology for coherent sheaves on \(Y\) equipped with a \(G\)-action. He can even handle the case in which the discrete group \(G\) acts on \(Y\) with fixed points (discrete co-compact action of \(G\) on \(Y)\) and the very important case in which on the sheaves acts a central extension of \(G\) by \(S^1\), obtaining a theory which contains the ``Vafa-Witten twisting trick'' introduced by Gromov. He obtains an Atiyah \(L^2\)-index theorem in this set-up.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 32J15
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 46L10
Mathematics Subject Classification ID: 58J20
zbMATH DE Number: 1502098
zbMATH Keywords: coherent analytic sheaves
zbMATH Keywords: complex spaces
zbMATH Keywords: \(L^2\)-cohomology groups
zbMATH Keywords: Galois covering
zbMATH Keywords: Atiyah's \(L^2\) index theorem
zbMATH Keywords: \(L^p\)-cohomology theory for coherent analytic sheaves
zbMATH Keywords: central extension by \(S^1\)
zbMATH Keywords: discrete co-compact action
MaRDI profile type: Publication
full work available at URL: pl00004413
OpenAlex ID: W2023786188
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description: scientific article; zbMATH DE number 1502098