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Abstract
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The Topological Period-Index Conjecture is a hypothesis which relates the period
and index of elements of the cohomological Brauer group of a space. It was identified
by Antieau and Williams as a topological analogue of the Period-Index Conjecture
for function fields.
In this paper we show that the Topological Period-Index Conjecture holds and is in general
sharp for spin
-manifolds. We also show that
it fails in general for
-manifolds.
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Keywords
Brauer groups, twisted $K$-theory, period-index problems
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Mathematical Subject Classification 2010
Primary: 57R19
Secondary: 14F22, 19L50
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Milestones
Received: 4 February 2020
Revised: 10 February 2020
Accepted: 25 February 2020
Published: 28 July 2020
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