Abstract A generalised Postnikov tower for a space X is a tower of principal fibrations with fibres generalised Eilenberg–MacLane spaces, whose inverse limit is weakly homotopy equivalent to X. In this paper we give a characterisation of a polyhedral product Z K ⁢ ( X , A ) {Z_{K}(X,A)} whose universal cover either admits a generalised Postnikov tower of finite length, or is a homotopy retract of a space admitting such a tower. We also include p-local and rational versions of the theorem. We end with a group theoretic application.

中文翻译：

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用有限广义 Postnikov 分解表征多面体产品

摘要 空间 X 的广义 Postnikov 塔是具有纤维广义 Eilenberg-MacLane 空间的主纤维的塔，其逆极限弱同伦等价于 X。在本文中，我们给出了多面体积 ZK ⁢ ( X , A ) {Z_{K}(X,A)} 其全覆盖要么接纳有限长度的广义 Postnikov 塔，要么是接纳这种塔的空间的同伦缩回。我们还包括定理的 p 局部和有理版本。我们以群论的应用结束。