Volume 9, issue 1 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The index of projective families of elliptic operators

Varghese Mathai, Richard B Melrose and Isadore M Singer

Geometry & Topology 9 (2005) 341–373

arXiv: math.DG/0206002

Abstract

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 K–theory of the parametrizing space, X. The main result is the equality of these two notions of index when the twisting class is in the torsion subgroup of H3(X; ). 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
Mathematical Subject Classification 2000
Primary: 19K56
Secondary: 58J20
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Publication
Received: 7 December 2004
Accepted: 28 February 2005
Published: 1 March 2005
Proposed: Tomasz Mrowka
Seconded: Ralph Cohen, Gang Tian
Authors
Varghese Mathai
Department of Pure Mathematics
University of Adelaide
Adelaide 5005
Australia
Richard B Melrose
Department of Mathematics
Massachusetts Institute of Technology
Cambridge
Massachusetts 02139
USA
Isadore M Singer
Department of Mathematics
Massachusetts Institute of Technology
Cambridge
Massachusetts 02139
USA