Polyhedral coproducts
Polyhedral coproducts
Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We begin a study of the basic properties of polyhedral coproducts, surveying the Eckmann--Hilton duals of various familiar examples and properties of polyhedral products. In particular, we show that polyhedral coproducts give a functorial interpolation between the wedge and cartesian product of spaces which differs from the one given by polyhedral products, and we establish a general loop space decomposition for these spaces which is dual to the suspension splitting of a polyhedral product due to Bahri, Bendersky, Cohen and Gitler.
Polyhedral products, homotopy limits, loop space decompositions
1781–1800
Stanton, Lewis R.
a8038748-d2cf-4d2c-b495-7db673edaeae
Amelotte, Steven
74a3acf5-3f97-4fd2-b3ee-aeaf06c835c9
Hornslien, William
3e52ecc7-cd29-4ae8-9d5b-d27de679fab5
Stanton, Lewis R.
a8038748-d2cf-4d2c-b495-7db673edaeae
Amelotte, Steven
74a3acf5-3f97-4fd2-b3ee-aeaf06c835c9
Hornslien, William
3e52ecc7-cd29-4ae8-9d5b-d27de679fab5
Stanton, Lewis R., Amelotte, Steven and Hornslien, William
(2026)
Polyhedral coproducts.
Algebraic and Geometric Topology, 26 (5), .
(doi:10.2140/agt.2026.26.1781).
Abstract
Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We begin a study of the basic properties of polyhedral coproducts, surveying the Eckmann--Hilton duals of various familiar examples and properties of polyhedral products. In particular, we show that polyhedral coproducts give a functorial interpolation between the wedge and cartesian product of spaces which differs from the one given by polyhedral products, and we establish a general loop space decomposition for these spaces which is dual to the suspension splitting of a polyhedral product due to Bahri, Bendersky, Cohen and Gitler.
Text
Polyhedral_Coproducts
- Accepted Manuscript
More information
Accepted/In Press date: 26 May 2025
e-pub ahead of print date: 23 May 2026
Keywords:
Polyhedral products, homotopy limits, loop space decompositions
Identifiers
Local EPrints ID: 503036
URI: http://eprints.soton.ac.uk/id/eprint/503036
ISSN: 1472-2747
PURE UUID: 51225569-0c87-4435-a4fa-e52cb06690a9
Catalogue record
Date deposited: 17 Jul 2025 16:45
Last modified: 20 Aug 2026 03:03
Export record
Altmetrics
Contributors
Author:
Lewis R. Stanton
Author:
Steven Amelotte
Author:
William Hornslien
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