Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/57322
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 Responsibility: | 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 www.arXiv.org in 2009 by Varghese Mathai. Post-print sourced from www.arxiv.org. |
Grant ID: | ARC |
Published version: | http://arxiv.org/abs/0809.0028 |
Appears in Collections: | Aurora harvest 5 Pure Mathematics publications |
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hdl_57322.pdf | 444.66 kB | Publisher's post-print | View/Open |
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