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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.19258 |
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| _version_ | 1866916773297651712 |
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| author | Amelotte, Steven Hornslien, William Stanton, Lewis |
| author_facet | Amelotte, Steven Hornslien, William Stanton, Lewis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19258 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polyhedral coproducts Amelotte, Steven Hornslien, William Stanton, Lewis Algebraic Topology 55P10, 55P35, 18A30, 55P30 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. |
| title | Polyhedral coproducts |
| topic | Algebraic Topology 55P10, 55P35, 18A30, 55P30 |
| url | https://arxiv.org/abs/2405.19258 |