## 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

### Keywords:

Brauer groups; twisted $$K$$-theory; period-index problems
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### References:

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