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Polyhedral
coproducts
Steven Amelotte, William Hornslien and Lewis Stanton |
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Algebraic & Geometric Topology 26 (2026) 1781–1800
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Abstract |
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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. |
Keywords
polyhedral products, homotopy limits, loop space
decompositions
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Mathematical Subject Classification
Primary: 55P10, 55P35
Secondary: 18A30, 55P30
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References |
Publication
Received: 6 June 2024
Revised: 24 April 2025
Accepted: 26 May 2025
Published: 23 May 2026
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Authors |
| Steven Amelotte | |
| School of Mathematics and
Statistics Carleton University Ottawa, ON Canada |
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| William Hornslien | |
| Institut Fourier Université Grenoble-Alpes Grenoble France |
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| Lewis Stanton | |
| School of Mathematical
Sciences University of Southampton Southampton United Kingdom |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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