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A NOTE ON BUNDLE GERBES AND INFINITE-DIMENSIONALITY

Part of: Global differential geometry

Published online by Cambridge University Press:  22 March 2011

MICHAEL MURRAY  and
DANNY STEVENSON
MICHAEL MURRAY*
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005, Australia (email: michael.murray@adelaide.edu.au)
DANNY STEVENSON
Affiliation:
Department of Mathematics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, UK (email: d.stevenson@maths.gla.ac.uk)
*
✉For correspondence; e-mail: michael.murray@adelaide.edu.au
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Abstract

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Let (P,Y ) be a bundle gerbe over a fibre bundle Y →M. We show that if M is simply connected and the fibres of Y →M are connected and finite-dimensional, then the Dixmier–Douady class of (P,Y ) is torsion. This corrects and extends an earlier result of the first author.

Keywords

bundle gerbesDixmier–Douady classinfinite-dimensionality

MSC classification

Secondary: 53C08: Gerbes, differential characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 90 , Issue 1 , February 2011 , pp. 81 - 92
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The first author acknowledges the support of the Australian Research Council.

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