The Topological Period-Index Conjecture for spinc 6-manifolds

Diarmuid John Crowley; Mark Grant

doi:10.2140/akt.2020.5.605

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

Diarmuid John Crowley, Mark Grant^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

University of Melbourne

Research output: Contribution to journal › Article › peer-review

2 Downloads (Pure)

Abstract

The Topological Period-Index Conjecture is an 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.

Original language	English
Pages (from-to)	605-620
Number of pages	17
Journal	Annals of K-Theory
Volume	5
Issue number	3
DOIs	https://doi.org/10.2140/akt.2020.5.605
Publication status	Published - 28 Feb 2020

Bibliographical note

**On publication email publisher and request a copy of PDF for repository - see https://msp.org/publications/policies/**

Access to Document

10.2140/akt.2020.5.605Licence: Unspecified

Grant_etal_akt_Topological_VOR
First published in Annals of K-Theory in Vol. 5 (2020), No. 3, published by Mathematical Sciences Publishers, © 2020 Mathematical Sciences Publishers
Final published version, 751 KBLicence: Other

https://arxiv.org/abs/1802.01296

Mark Grant
- School of Natural & Computing Sciences, Mathematical Science - Senior Lecturer
Person: Academic

Cite this

@article{11b044f7123f407eac8ebdfe1f7b0419,

title = "The Topological Period-Index Conjecture for spinc 6-manifolds",

abstract = "The Topological Period-Index Conjecture is an 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.",

author = "Crowley, {Diarmuid John} and Mark Grant",

note = "**On publication email publisher and request a copy of PDF for repository - see https://msp.org/publications/policies/**",

year = "2020",

month = feb,

day = "28",

doi = "10.2140/akt.2020.5.605",

language = "English",

volume = "5",

pages = "605--620",

journal = "Annals of K-Theory",

issn = "2379-1683",

publisher = "Mathematical Sciences Publishers",

number = "3",

}

TY - JOUR

T1 - The Topological Period-Index Conjecture for spinc 6-manifolds

AU - Crowley, Diarmuid John

AU - Grant, Mark

N1 - **On publication email publisher and request a copy of PDF for repository - see https://msp.org/publications/policies/**

PY - 2020/2/28

Y1 - 2020/2/28

N2 - The Topological Period-Index Conjecture is an 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.

AB - The Topological Period-Index Conjecture is an 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.

U2 - 10.2140/akt.2020.5.605

DO - 10.2140/akt.2020.5.605

M3 - Article

SN - 2379-1683

VL - 5

SP - 605

EP - 620

JO - Annals of K-Theory

JF - Annals of K-Theory

IS - 3

ER -

The Topological Period-Index Conjecture for spinc 6-manifolds

Abstract

Bibliographical note

Access to Document

Fingerprint

Profiles

Mark Grant

Cite this

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