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• W2962966125 abstract "Inspired by recent papers on twisted <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper K> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=application/x-tex>K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-theory, we consider in this article the question of when a twist <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper R> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>R</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {R}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> over a locally compact Hausdorff groupoid <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> (with unit space a CW-complex) admits a twisted vector bundle, and we relate this question to the Brauer group of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that the twists which admit twisted vector bundles give rise to a subgroup of the Brauer group of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. When <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an étale groupoid, we establish conditions (involving the classifying space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper B script upper G> <mml:semantics> <mml:mrow> <mml:mi>B</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>G</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>Bmathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) which imply that a torsion twist <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper R> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>R</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {R}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper G> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> admits a twisted vector bundle." @default.
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• W2962966125 date "2016-05-06" @default.
• W2962966125 modified "2023-09-27" @default.
• W2962966125 title "Twists over étale groupoids and twisted vector bundles" @default.
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• W2962966125 doi "https://doi.org/10.1090/proc/13165" @default.
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