The University of Southampton
University of Southampton Institutional Repository

The dual polyhedral product, cocategory and nilpotence

The dual polyhedral product, cocategory and nilpotence
The dual polyhedral product, cocategory and nilpotence

The notion of a dual polyhedral product is introduced as a generalization of Hovey's definition of Lusternik–Schnirelmann cocategory. Properties established from homotopy decompositions that relate the based loops on a polyhedral product to the based loops on its dual are used to show that if X is a simply-connected space then the weak cocategory of X equals the homotopy nilpotency class of ΩX. This answers a fifty year old problem posed by Ganea. The methods are applied to determine the homotopy nilpotency class of quasi-p-regular exceptional Lie groups and sporadic p-compact groups.

polyhedral product, thin product, cocategory, Whitehead product, homotopy nilpotence
0001-8708
138-192
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80

Theriault, Stephen (2018) The dual polyhedral product, cocategory and nilpotence. Advances in Mathematics, 340, 138-192. (doi:10.1016/j.aim.2018.09.037).

Record type: Article

Abstract

The notion of a dual polyhedral product is introduced as a generalization of Hovey's definition of Lusternik–Schnirelmann cocategory. Properties established from homotopy decompositions that relate the based loops on a polyhedral product to the based loops on its dual are used to show that if X is a simply-connected space then the weak cocategory of X equals the homotopy nilpotency class of ΩX. This answers a fifty year old problem posed by Ganea. The methods are applied to determine the homotopy nilpotency class of quasi-p-regular exceptional Lie groups and sporadic p-compact groups.

Text
Cocat_Nilpotence.pdf - Author's Original
Restricted to Repository staff only
Request a copy
Text
20/Cocat_Nilpotence_revised2 - Accepted Manuscript
Download (534kB)

More information

Accepted/In Press date: 20 September 2018
e-pub ahead of print date: 10 October 2018
Published date: 15 December 2018
Keywords: polyhedral product, thin product, cocategory, Whitehead product, homotopy nilpotence
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 396696
URI: http://eprints.soton.ac.uk/id/eprint/396696
ISSN: 0001-8708
PURE UUID: 3c9a9350-8283-4e8e-a04a-ff618cd8b0ba
ORCID for Stephen Theriault: ORCID iD orcid.org/0000-0002-7729-5527

Catalogue record

Date deposited: 13 Jun 2016 13:56
Last modified: 15 Mar 2024 05:39

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×