On the non-existence of free \(\mathcal A_d\)-actions on products of spheres
type: Item
instance of: scholarly article
zbMATH Open document ID: 1269.57015
author: Zbigniew Błaszczyk
published in: Mathematische Nachrichten
publication date: 2012-05-14T00:00:00Z
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 6034379
zbMATH Keywords: group
zbMATH Keywords: free action
zbMATH Keywords: product of spheres
MaRDI profile type: Publication
full work available at URL: mana.201000079
OpenAlex ID: W2234617169
cites work: Q4656980
cites work: Fixity and free group actions on products of spheres
cites work: Periodic complexes and group actions
cites work: Complexity and multiple complexes
cites work: Q5340151
cites work: Q4002278
cites work: The representation theory of the symmetric groups
cites work: Transformation groups on \(S^ n\times\mathbb{R}^ m\)
DOI: 10.1002/MANA.201000079
title: On the non-existence of free \(\mathcal A_d\)-actions on products of spheres
review text: The paper investigates the well known problem of the existence of a free group action on a product of spheres. The main result states that the alternating group \(A_p\), where \(p\geq 7\) is a prime number, does not act on a space whose integral homology is isomorphic to that of the product of \(p\) copies of \(S^n\). The main technique of the proof is to investigate integral representations of cyclic groups of prime order and to use Bob Oliver's result on the action of \(A_4\) on the product of two spheres.
reviewed by: Jarek Kȩdra
description: scientific article; zbMATH DE number 6034379