#### Geometry & Topology, Vol. 9 (2005)
Paper no. 11, pages 341--373.

## The index of projective families of elliptic operators

### Varghese Mathai, Richard B Melrose, Isadore M Singer

**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
H^3(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

**AMS subject classification**.
Primary: 19K56.
Secondary: 58J20.

**DOI:** 10.2140/gt.2005.9.341

**E-print:** `arXiv:math.DG/0206002`

Submitted to GT on 7 December 2004.
Paper accepted 28 February 2005.
Paper published 1 March 2005.

Notes on file formats
Varghese Mathai, Richard B Melrose, Isadore M Singer

Department of Pure Mathematics, University of Adelaide

Adelaide 5005, Australia

Department of Mathematics, Massachusetts Institute of Technology

Cambridge, Mass 02139, USA

Department of Mathematics, Massachusetts Institute of Technology

C
ambridge, Mass 02139, USA

Email: vmathai@maths.adelaide.edu.au, rbm@math.mit.edu, ims@math.mit.edu

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