Volume 9, issue 1 (2005)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
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
References
Forward citations
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