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Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class

Published online by Cambridge University Press:  11 September 2014

Antti J. Harju  and
Jouko Mickelsson
Antti J. Harju
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, Finland
Jouko Mickelsson
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, Finland, [email protected]
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Abstract

Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on and an integral class in H2(M,ℤ). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups.

Keywords

Twisted K-TheoryGerbeHamiltonian Quantization19L5053C0881T70
Type
Research Article
Information
Journal of K-Theory , Volume 14 , Issue 2 , October 2014 , pp. 247 - 272
Copyright
Copyright © ISOPP 2014 

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