Characterisation of polyhedral products with finite generalised Postnikov decomposition

Kouyemon Iriye; Daisuke Kishimoto; Ran Levi

doi:10.1515/forum-2020-0059

Characterisation of polyhedral products with finite generalised Postnikov decomposition

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

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1253–1269
Number of pages	14
Journal	Forum Mathematicum
Volume	32
Issue number	5
Early online date	19 May 2020
DOIs	https://doi.org/10.1515/forum-2020-0059
Publication status	Published - 1 Sept 2020

Bibliographical note

Funding Source: Japan Society for the Promotion of Science
Award identifier / Grant number: 19K03473
Award identifier / Grant number: 17K05248
Funding Source: Engineering and Physical Sciences Research Council
Award identifier / Grant number: EP/P025072/1

Keywords

polyhedral product
Postnikov tower
generalised Postnikov tower
graph product of groups
Polyhedral product
SPACE
COMPLEXES
HOMOTOPY-GROUPS

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Cite this

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Characterisation of polyhedral products with finite generalised Postnikov decomposition

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Keywords

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