Twistings of KR for Real groupoids
El-ka\"ioum M. Moutuou
TL;DR
This paper introduces a new framework for twistings of KR-theory over real groupoids using Real graded Dixmier-Douady bundles, connecting it to equivariant cohomology and groupoid extensions.
Contribution
It defines the Real graded Brauer group for groupoids with involution and interprets it via groupoid extensions and equivariant cohomology, advancing the understanding of KR-theory twistings.
Findings
Defined B-fields as Real graded Dixmier-Douady bundles.
Constructed the Real graded Brauer group for groupoids with involution.
Outlined the twisted KR-functor in this setting.
Abstract
B-fields over a groupoid with involution are defined as Real graded Dixmier-Douady bundles. We use these to introduce the Real graded Brauer group which constitutes the set of twistings for Atiyah's KR-functor in the category of locally compact groupoids with involutions. We interpret this group in terms of groupoid extensions and elements of some equivariant Cech cohomology theory. The construction of the twisted KR-functor is outlined.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Geometry