Group actions on finite CW-complexes
type: Item
instance of: scholarly article
title: Group actions on finite CW-complexes
zbMATH Open document ID: 0785.57016
author: Mashhoor Refai
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1994-04-21T00:00:00Z
review text: A lot of people have worked on some version of the following conjecture: Let \((\mathbb{Z}/2)^ l\) act freely and cellularly on a CW-complex that is homotopy equivalent to a product of \(m\) spheres. Then \(l\leq m\). (The author gets the inequality wrong in his statement in the introduction.) G. Carlsson showed that \(l\geq 3\) implies \(m\geq 3\). The author pushes Carlsson's calculations one step further to show that \(l\geq 4\) implies \(m\geq 4\). In fact, he shows that the dimension of the \(\mathbb{Z}/2\)- cohomology of a finite CW-complex \(X\) on which \((\mathbb{Z}/2)^ l\) acts freely and cellularly, has to be even and at least 10.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 18G20
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 18G35
zbMATH DE Number: 202460
zbMATH Keywords: elementary abelian 2-group
zbMATH Keywords: free action
zbMATH Keywords: differential graded module
zbMATH Keywords: homological dimension
reviewed by: Martin Raussen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 202460