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https://hdl.handle.net/2440/57322
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DC Field | Value | Language |
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dc.contributor.author | Varghese, M. | - |
dc.contributor.author | Melrose, R. | - |
dc.contributor.author | Singer, I. | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | Asterisque, 2009; 328(328):255-296 | - |
dc.identifier.issn | 0303-1179 | - |
dc.identifier.uri | http://hdl.handle.net/2440/57322 | - |
dc.description.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. | - |
dc.description.statementofresponsibility | V. Mathai, R.B. Melrose and I.M. Singer | - |
dc.language.iso | en | - |
dc.publisher | Soc Mathematique France | - |
dc.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. | - |
dc.source.uri | http://arxiv.org/abs/0809.0028 | - |
dc.subject | Twisted K-theory | - |
dc.subject | index theorem | - |
dc.subject | decomposable Dixmier-Douady invariant | - |
dc.subject | smooth Azumaya bundle | - |
dc.subject | Chern Character | - |
dc.subject | twisted cohomology | - |
dc.title | The index of projective families of elliptic operators: the decomposable case | - |
dc.type | Journal article | - |
dc.relation.grant | ARC | - |
pubs.publication-status | Published | - |
dc.identifier.orcid | Varghese, M. [0000-0002-1100-3595] | - |
Appears in Collections: | Aurora harvest 5 Pure Mathematics publications |
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File | Description | Size | Format | |
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hdl_57322.pdf | 444.66 kB | Publisher's post-print | View/Open |
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