Varghese, M.Melrose, R.Singer, I.2010-04-062010-04-062009Asterisque, 2009; 328(328):255-2960303-1179http://hdl.handle.net/2440/57322An 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.enCopyright © 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.Twisted K-theoryindex theoremdecomposable Dixmier-Douady invariantsmooth Azumaya bundleChern Charactertwisted cohomologyJournal article002009492300020801660000836089Varghese, M. [0000-0002-1100-3595]