New York Journal of Mathematics
Volume 29 (2023), 147-170


Simon Kitson

A semi-equivariant Dixmier-Douady invariant

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Published: January 22, 2023.
Keywords: Dixmier-Douady invariant, equivariant cohomology, orientifold, anti-linear, Real vector bundle, KR-theory.
Subject [2010]: 55N91.

A generalisation of the equivariant Dixmier-Douady invariant is constructed as a second-degree cohomology class within a new semi-equi-variant Cech cohomology theory. This invariant obstructs liftings of semi-equivariant principal bundles that are associated to central exact sequences of structure groups in which each structure group is acted on by the equivariance group. The results and methods described can be applied to the study of complex vector bundles equipped with linear/anti-linear actions, such as Atiyah's Real vector bundles.



Author information

Simon Kitson:
Mathematical Sciences Institute
Australian National University
Canberra ACT 2601, Australia