On F\'elix-Tanr\'e rational models for polyhedral products

Katsuhiko Kuribayashi

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arXiv · 2310.09205

On F\'elix-Tanr\'e rational models for polyhedral products

Katsuhiko Kuribayashi

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Abstract

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.

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Katsuhiko Kuribayashi. 2023-10-13. On F\'elix-Tanr\'e rational models for polyhedral products. https://arxiv.org/abs/2310.09205

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