On Félix-Tanré rational models for polyhedral products
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917799251673088 |
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| author | Kuribayashi, Katsuhiko |
| author_facet | Kuribayashi, Katsuhiko |
| contents | The Félix-Tanré rational model for the polyhedral product of a fibre inclusion is considered. In particular, we investigate the rational model for the polyhedral product of a pair of Lie groups corresponding to arbitrary simplicial complex and the rational homotopy group of the polyhedral product. Furthermore, it is proved that for a partial quotient $N$ associated with a toric manifold $M$, the following conditions are equivalent: (i) $N=M$. (ii) The odd-degree rational cohomology of $N$ is trivial. (iii) The torus bundle map from $N$ to the Davis-Januszkiewicz space is formalizable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09205 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Félix-Tanré rational models for polyhedral products Kuribayashi, Katsuhiko Algebraic Topology 13F55, 55P62, 57S12 The Félix-Tanré rational model for the polyhedral product of a fibre inclusion is considered. In particular, we investigate the rational model for the polyhedral product of a pair of Lie groups corresponding to arbitrary simplicial complex and the rational homotopy group of the polyhedral product. Furthermore, it is proved that for a partial quotient $N$ associated with a toric manifold $M$, the following conditions are equivalent: (i) $N=M$. (ii) The odd-degree rational cohomology of $N$ is trivial. (iii) The torus bundle map from $N$ to the Davis-Januszkiewicz space is formalizable. |
| title | On Félix-Tanré rational models for polyhedral products |
| topic | Algebraic Topology 13F55, 55P62, 57S12 |
| url | https://arxiv.org/abs/2310.09205 |