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The
Topological Period-Index Conjecture for spin$^c$
$6$-manifolds
Diarmuid Crowley and Mark Grant |
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Vol. 5 (2020), No. 3, 605–620
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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. |
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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Authors |
| Diarmuid Crowley | |
| School of Mathematics and
Statistics The University of Melbourne Parkville Australia |
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| Mark Grant | |
| Institute of Mathematics University of Aberdeen Aberdeen United Kingdom |
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