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Crowley, Diarmuid; Grant, Mark

The topological period-index conjecture for \(\mathrm{spin}^c\) 6-manifolds. (English) Zbl 1440.57033

Ann. \(K\)-Theory 5, No. 3, 605-620 (2020).
Summary: 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 \(\mathrm{spin}^c\) 6-manifolds. We also show that it fails in general for \(6\)-manifolds.

MSC:

57R19 Algebraic topology on manifolds and differential topology
14F22 Brauer groups of schemes
19L50 Twisted \(K\)-theory; differential \(K\)-theory

Keywords:

Brauer groups; twisted \(K\)-theory; period-index problems
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\textit{D. Crowley} and \textit{M. Grant}, Ann. \(K\)-Theory 5, No. 3, 605--620 (2020; Zbl 1440.57033)
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