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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.

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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: https://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: 23 Sep 2019 18:23

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