Geometry & Topology 9 (2005) 341–373

DOI: 10.2140/gt.2005.9.341

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;Z). 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

Primary: 19K56

Secondary: 58J20

References

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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