The index of projective families of elliptic operators: the decomposable case

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dc.contributor.authorVarghese, M.
dc.contributor.authorMelrose, R.
dc.contributor.authorSinger, I.
dc.date.issued2009
dc.description.abstractAn 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.
dc.description.statementofresponsibilityV. Mathai, R.B. Melrose and I.M. Singer
dc.identifier.citationAsterisque, 2009; 328(328):255-296
dc.identifier.issn0303-1179
dc.identifier.orcidVarghese, M. [0000-0002-1100-3595]
dc.identifier.urihttp://hdl.handle.net/2440/57322
dc.language.isoen
dc.publisherSoc Mathematique France
dc.relation.grantARC
dc.rightsCopyright © 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.
dc.source.urihttp://arxiv.org/abs/0809.0028
dc.subjectTwisted K-theory
dc.subjectindex theorem
dc.subjectdecomposable Dixmier-Douady invariant
dc.subjectsmooth Azumaya bundle
dc.subjectChern Character
dc.subjecttwisted cohomology
dc.titleThe index of projective families of elliptic operators: the decomposable case
dc.typeJournal article
pubs.publication-statusPublished

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