×

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

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
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] 10.2140/gt.2014.18.1115 · Zbl 1288.19006 · doi:10.2140/gt.2014.18.1115
[2] 10.1112/jtopol/jtt042 · Zbl 1299.14018 · doi:10.1112/jtopol/jtt042
[3] 10.1007/978-1-4684-9327-6 · doi:10.1007/978-1-4684-9327-6
[4] ; Colliot-Thélène, Enseign. Math. (2), 48, 127 (2002) · Zbl 1047.16007
[5] 10.1090/gsm/035 · doi:10.1090/gsm/035
[6] 10.1007/978-3-642-67821-9 · doi:10.1007/978-3-642-67821-9
[7] ; Donovan, Inst. Hautes Études Sci. Publ. Math., 38, 5 (1970) · Zbl 0207.22003
[8] 10.1112/blms/bds090 · Zbl 1270.57068 · doi:10.1112/blms/bds090
[9] 10.4310/HHA.2006.v8.n2.a5 · Zbl 1107.55003 · doi:10.4310/HHA.2006.v8.n2.a5
[10] ; Grothendieck, Dix exposés sur la cohomologie des schémas. Adv. Stud. Pure Math., 3, 46 (1968) · Zbl 0193.21503
[11] 10.1112/topo.12119 · Zbl 1441.55014 · doi:10.1112/topo.12119
[12] 10.1215/S0012-7094-04-12313-9 · Zbl 1060.14025 · doi:10.1215/S0012-7094-04-12313-9
[13] 10.1090/S0002-9904-1961-10690-3 · Zbl 0192.29601 · doi:10.1090/S0002-9904-1961-10690-3
[14] ; Morgan, The Seiberg-Witten equations and applications to the topology of smooth four-manifolds. Mathematical Notes, 44 (1996) · Zbl 0846.57001
[15] 10.1093/acprof:oso/9780198509240.001.0001 · doi:10.1093/acprof:oso/9780198509240.001.0001
[16] 10.2307/2160595 · Zbl 0858.57033 · doi:10.2307/2160595
[17] 10.1007/BF02566923 · Zbl 0057.15502 · doi:10.1007/BF02566923
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.