Characterisation of polyhedral products with finite generalised Postnikov decomposition

Kouyemon Iriye, Daisuke Kishimoto* (Corresponding Author), Ran Levi

*Corresponding author for this work

Research output: Contribution to journalArticle

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 $Z_K(X,A)$ 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.
Original languageEnglish
Pages (from-to)1253–1269
Number of pages14
JournalForum Mathematicum
Volume32
Issue number5
Early online date19 May 2020
DOIs
Publication statusPublished - 1 Sep 2020

Keywords

  • polyhedral product
  • Postnikov tower
  • generalised Postnikov tower
  • graph product of groups
  • Polyhedral product

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