Fonctorialité en K-théorie bivariante pour les variétés lipschitziennes. (Functoriality in the bivariant K-theory for Lipschitz manifolds)
type: Item
instance of: scholarly article
title: Fonctorialité en K-théorie bivariante pour les variétés lipschitziennes. (Functoriality in the bivariant K-theory for Lipschitz manifolds)
zbMATH Open document ID: 0702.57008
DOI: 10.1007/BF00534136
author: Michel Hilsum
published in: \(K\)-Theory
publication date: 1989-01-01T00:00:00Z
review text: Soit f: \(M\to V/F\) un morphisme continue orienté d'une variété lipschitzienne M dans l'espace des feuilles d'une variété lipschitzienne feuilletée (V,F), et soit \(C^*(V,F)\) la \(C^*\)- algèbre du feuilletage d'A. Connes. On construit un élément \(\Sigma\) (f) dans le groupe de K-théorie bivariante \(KK(C_ 0(M)\); \(C^*(V,F))\) de G. G. Kasparov et on montre la fonctorialité de cette construction. Ceci répond pour les variétés lipschitziennes à une conjecture d'A. Connes, résolue pour les variétés différentiables. Dans le cas particulier où V/F est un point, cet élément est la classe dans \(K_ 0(M)\) de l'opérateur de signature construit par N. Teleman.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 18F25
Mathematics Subject Classification ID: 19K35
zbMATH DE Number: 4151392
zbMATH Keywords: foliated Lipschitz manifolds
zbMATH Keywords: maps into spaces of leaves
zbMATH Keywords: Kasparov K- theory
zbMATH Keywords: \(C^ *\)-algebra of a foliated manifold
zbMATH Keywords: signature operator
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00534136
OpenAlex ID: W2334724188
description: scientific article; zbMATH DE number 4151392