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The
index of projective families of elliptic operators
Varghese Mathai, Richard B Melrose and Isadore M Singer |
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Geometry & Topology 9 (2005) 341–373
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arXiv: math.DG/0206002 |
Abstract |
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An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted –theory of the parametrizing space, . The main result is the equality of these two notions of index when the twisting class is in the torsion subgroup of . The Chern character of the index class is then computed. |
Keywords
projective vector bundles, twisted $K$–theory, projective
families of elliptic operators, Index theorem, determinant
lines, twisted Chern character
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Mathematical Subject Classification 2000
Primary: 19K56
Secondary: 58J20
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References |
Forward citations |
Publication
Received: 7 December 2004
Accepted: 28 February 2005
Published: 1 March 2005
Proposed: Tomasz Mrowka
Seconded: Ralph Cohen, Gang Tian
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Authors |
| Varghese Mathai | |
| Department of Pure Mathematics University of Adelaide Adelaide 5005 Australia |
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| Richard B Melrose | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA |
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| Isadore M Singer | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA |
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