The Topological Period-Index Conjecture for spin$^c$ $6$-manifolds

Abstract

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${}^c$ $6$-manifolds. We also show that it fails in general for $6$-manifolds.