Suspension splittings of 5-dimensional Poincaré duality complexes and their applications
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908776643166208 |
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| author | Amelotte, Steven Cutler, Tyrone So, Tseleung |
| author_facet | Amelotte, Steven Cutler, Tyrone So, Tseleung |
| contents | Let $X$ be a connected, orientable, 5-dimensional Poincaré duality complex with torsion-free $H_1(X;\mathbb{Z})$. We show that $ΣX$ is homotopy equivalent to a wedge of recognisable spaces and study to what extent its homotopy type is determined by algebraic data. These results are then used to compute the unstable cohomotopy groups $π^3(X)$ and $π^3(X;\mathbb{Z}/k)$ as well as give partial information about the cohomotopy set $π^2(X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16073 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Suspension splittings of 5-dimensional Poincaré duality complexes and their applications Amelotte, Steven Cutler, Tyrone So, Tseleung Algebraic Topology 57P10, 55P15, 57N65 Let $X$ be a connected, orientable, 5-dimensional Poincaré duality complex with torsion-free $H_1(X;\mathbb{Z})$. We show that $ΣX$ is homotopy equivalent to a wedge of recognisable spaces and study to what extent its homotopy type is determined by algebraic data. These results are then used to compute the unstable cohomotopy groups $π^3(X)$ and $π^3(X;\mathbb{Z}/k)$ as well as give partial information about the cohomotopy set $π^2(X)$. |
| title | Suspension splittings of 5-dimensional Poincaré duality complexes and their applications |
| topic | Algebraic Topology 57P10, 55P15, 57N65 |
| url | https://arxiv.org/abs/2311.16073 |