The index of projective families of elliptic operators: the decomposable case
Date
2009
Authors
Varghese, M.
Melrose, R.
Singer, I.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Asterisque, 2009; 328(328):255-296
Statement of Responsibility
V. Mathai, R.B. Melrose and I.M. Singer
Conference Name
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.
School/Discipline
Dissertation Note
Provenance
Description
Access Status
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.