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
Stanton, Lewis Richard
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Amelotte, Steven
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Hornslien, William
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Stanton, Lewis Richard
bb6aed52-6a94-403f-a87e-5d7b7a6c8152
Amelotte, Steven
74a3acf5-3f97-4fd2-b3ee-aeaf06c835c9
Hornslien, William
3e52ecc7-cd29-4ae8-9d5b-d27de679fab5
Stanton, Lewis Richard, Amelotte, Steven and Hornslien, William
(2025)
Polyhedral coproducts.
Algebraic and Geometric Topology.
(In Press)
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
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
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Date deposited: 17 Jul 2025 16:45
Last modified: 18 Jul 2025 02:08
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Contributors
Author:
Lewis Richard Stanton
Author:
Steven Amelotte
Author:
William Hornslien
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