The longitudinal index theorem for foliations
type: Item
instance of: scholarly article
title: The longitudinal index theorem for foliations
zbMATH Open document ID: 0575.58030
author: Georges Skandalis
author: Alain Connes
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1984-01-01T00:00:00Z
review text: A topological formula for the analytical index of a differential operator D elliptic along the leaves of the foliation (V,F) is given. The index in the Atiyah-Singer theorem for families is an element of the \(K^ 0(B)=K_ 0(C(B))\), where B is the basic space of the fibration. On the case of foliations the algebra C(B) is replaced by a canonically defined \(C^*\)-algebra \(C^*(V;F)\) and \(ind(D)\in K_ 0(C^*(V;F))\). The Kasparov K-bifunctor is a basic tool to prove the results of the paper.
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 37C85
zbMATH DE Number: 3919417
zbMATH Keywords: index theorem
zbMATH Keywords: longitudinal elliptic operator
zbMATH Keywords: analytical index of a differential operator
zbMATH Keywords: Atiyah-Singer theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195180375
OpenAlex ID: W2027992356
Wikidata QID: Q102038472
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DOI: 10.2977/PRIMS/1195180375
description: scientific article; zbMATH DE number 3919417