Vol. 5, No. 3, 2020

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

Diarmuid Crowley and Mark Grant

Vol. 5 (2020), No. 3, 605–620
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 spinc 6-manifolds. We also show that it fails in general for 6-manifolds.

Keywords
Brauer groups, twisted $K$-theory, period-index problems
Mathematical Subject Classification 2010
Primary: 57R19
Secondary: 14F22, 19L50
Milestones
Received: 4 February 2020
Revised: 10 February 2020
Accepted: 25 February 2020
Published: 28 July 2020
Authors
Diarmuid Crowley
School of Mathematics and Statistics
The University of Melbourne
Parkville
Australia
Mark Grant
Institute of Mathematics
University of Aberdeen
Aberdeen
United Kingdom