Which H-spaces are manifolds? I
type: Item
instance of: scholarly article
title: Which H-spaces are manifolds? I
zbMATH Open document ID: 0684.57014
DOI: 10.1016/0040-9383(88)90017-1
author: Shmuel Weinberger
author: Sylvain Cappell
published in: Topology
publication date: 1988-01-01T00:00:00Z
review text: The authors are concerned with the question whether a finite dimensional H-space is of the homotopy type of a closed manifold. This is a question first formulated and studied by W. Browder, who showed that the answer is positive when X is simply connected. In this article, the authors show that the answer is also positive when the fundamental group \(\pi_ 1(X,*)\) is either an odd p-group or infinite with at most cyclic 2- torsion. They also study the case when \(\pi_ 1(X,*)\) has only 2- torsion, and they give examples, when \(\pi_ 1(X,*)\cong {\mathbb{Z}}_ 2\times {\mathbb{Z}}_ 2\), of Poincaré complexes X not homotopy equivalent to closed manifolds.
Mathematics Subject Classification ID: 57R65
Mathematics Subject Classification ID: 57R19
Mathematics Subject Classification ID: 55P45
zbMATH DE Number: 4121043
zbMATH Keywords: finite dimensional H-space
zbMATH Keywords: homotopy type of a closed manifold
zbMATH Keywords: fundamental group
reviewed by: S. Y. Husseini
MaRDI profile type: Publication
full work available at URL: 0040-9383(88)90017-1
OpenAlex ID: W2080316912
description: scientific article; zbMATH DE number 4121043