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|a Mathai, V.
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a Melrose, Richard B
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|a Singer, Isadore Manuel
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|a Melrose, Richard B
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|a Singer, Isadore Manuel
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|a The index of projective families of elliptic operators: The decomposable case
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|b Société mathématique de France,
|c 2018-06-11T14:19:09Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/116193
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|a An index theory for projective families of elliptic pseudodiffer-ential operators is developed under two conditions. First, that the twisting, i.e. Dixmier-Douady, class is in H² (Xℤ) ∪ H¹ (X; Z) ⊂ H³ (Zℤ) 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.
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|a National Science Foundation (U.S.) (grant DMS0408993)
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