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Type: Journal article
Title: The index of projective families of elliptic operators: the decomposable case
Author: Varghese, M.
Melrose, R.
Singer, I.
Citation: Asterisque, 2009; 328(328):255-296
Publisher: Soc Mathematique France
Issue Date: 2009
ISSN: 0303-1179
Statement of
V. Mathai, R.B. Melrose and I.M. Singer
Abstract: An index theory for projective families of elliptic pseudodifferential operators is developed under two conditions. First, that the twisting, i.e. Dixmier-Douady, class is in H2(X; Z)[H1(X; Z) H3(X; Z) and secondly that the 2-class part is trivialized on the total space of the fibration. One of the features of this special case is that the corresponding Azumaya bundle can be refined to a bundle of smoothing operators. The topological and the analytic index of a projective family of elliptic operators associated with the smooth Azumaya bundle both take values in twisted K-theory of the parameterizing space and the main result is the equality of these two notions of index. The twisted Chern character of the index class is then computed by a variant of Chern-Weil theory.
Keywords: Twisted K-theory
index theorem
decomposable Dixmier-Douady invariant
smooth Azumaya bundle
Chern Character
twisted cohomology
Rights: Copyright © 2009. Societe Mathematique France All rights reserved. Submitted to Cornell University’s online archive in 2009 by Varghese Mathai. Post-print sourced from
Grant ID: ARC
Published version:
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