On F\'elix-Tanr\'e rational models for polyhedral products
The F\'elix-Tanr\'e 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 polyhed...
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creator | Kuribayashi, Katsuhiko |
description | The F\'elix-Tanr\'e 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. |
doi_str_mv | 10.48550/arxiv.2310.09205 |
format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.2310.09205</identifier><language>eng</language><subject>Mathematics - Algebraic Topology</subject><creationdate>2023-10</creationdate><rights>http://creativecommons.org/licenses/by-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2310.09205$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2310.09205$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kuribayashi, Katsuhiko</creatorcontrib><title>On F\'elix-Tanr\'e rational models for polyhedral products</title><description>The F\'elix-Tanr\'e 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
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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.</abstract><doi>10.48550/arxiv.2310.09205</doi><oa>free_for_read</oa></addata></record> |
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subjects | Mathematics - Algebraic Topology |
title | On F\'elix-Tanr\'e rational models for polyhedral products |
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