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|Type: ||Journal article|
|Title: ||The index of projective families of elliptic operators: the decomposable case|
|Author: ||Varghese, Mathai|
Melrose, Richard B.
Singer, Isadore M.
|Citation: ||Astérisque, 2009; 328:255-296|
|Publisher: ||Societe mathematique de France|
|Issue Date: ||2009|
|School/Discipline: ||School of Mathematical Sciences : Pure Mathematics|
|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.|
|Published version: ||http://arxiv.org/abs/0809.0028|
|Appears in Collections:||Pure Mathematics publications|
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