On Félix–Tanré rational models for polyhedral products

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 on 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.