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The analytic index of elliptic pseudodifferential operators on a singular foliation

Published online by Cambridge University Press:  10 March 2011

Iakovos Androulidakis  and
Georges Skandalis
Iakovos Androulidakis
Affiliation:
Georg-August Universität Göttingen, Mathematisches Institut, Bunsenstrasse 3-5, D-37073 Göttingen, Germany, iakovos@uni-math.gwdg.de
Georges Skandalis
Affiliation:
Université Paris Diderot (Paris 7) - CNRS, Institut de Mathématiques de Jussieu, UMR 7586 175, rue du Chevaleret, F-75013 Paris, France, skandal@math.jussieu.fr
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Abstract

In previous papers ([1, 2]) we defined the C*-algebra and the longitudinal pseudodifferential calculus of any singular foliation (M,). In the current paper we construct the analytic index of an elliptic operator as a KK-theory element, and prove that this element can be obtained from an “adiabatic foliation” on M×ℝ, which we introduce here.

Keywords

analytic indexfoliationsdeformationC*-algebra.

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Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 3 , December 2011 , pp. 363 - 385
Copyright
Copyright © ISOPP 2011

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