Teleman localization of Hochschild homology in a singular setting
type: Item
instance of: scholarly article
title: Teleman localization of Hochschild homology in a singular setting
zbMATH Open document ID: 1184.55002
DOI: 10.1134/S1061920809030078
published in: Russian Journal of Mathematical Physics
publication date: 2009-11-10T00:00:00Z
review text: Generalizations of the Hochschild-Kostant-Rosenberg theorem to singular spaces are considered. In particular, given a singular variety \(X\) with isolated singularities, the authors define a smooth intersection function algebra \(IC^\infty(X)\). This is defined as an algebra of smooth functions on the regular part of \(X\) which satisfy certain growth conditions near the singularities. The main theorem of the paper states that that the closed Hochschild homology of this algebra with coefficients in a suitable module (depending on a parameter \(\delta\)) is isomorphic to a certain ``intersection'' complex of differential forms, and the cohomology of the latter is the intersection cohomology of \(X\) (with perversity determined by \(\delta\)). Closed Hochschild homology here means that one divides the space of Hochschild cycles by the \textit{closure} of the space of Hochschild boundaries. Another often used terminology for this construction is \textit{reduced} cohomology. The identification of Hochschild homology with a suitable complex of differential forms is called ``Teleman localization'' in the paper. In addition to the above localization result, the paper also shows that such localization results hold for suitable algebras of functions on a manifold with boundary.
reviewed by: Thomas Schick
Mathematics Subject Classification ID: 55N33
Mathematics Subject Classification ID: 19D55
zbMATH DE Number: 5628086
zbMATH Keywords: Hochschild homology
zbMATH Keywords: Hochschild-Kostant-Rosenberg theorem
zbMATH Keywords: isolated singularities
author: Jean-Paul Brasselet
author: André Legrand
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5628086