The Lusternik-Schnirelmann category of certain infinite CW-complexes
type: Item
instance of: scholarly article
title: The Lusternik-Schnirelmann category of certain infinite CW-complexes
zbMATH Open document ID: 0933.55004
DOI: 10.1016/S0040-9383(98)00060-3
author: Joseph Roitberg
published in: Topology
publication date: 2000-04-04T00:00:00Z
review text: The author settles in the negative two questions concerning \(\text{cat}(X)\). First of all the LS-category of a 1-connected finite type CW-complex \(X\) which is the homotopy colimit of a sequence \(X_1\to X_2\to X_3\to\cdots\) of 1-connected finite CW-complexes may exceed the LS-category of each \(X_i\). For instance, the category of the mapping cone \(X\) of an essential phanton map \(f:\sum k(Z,5)\to S^4\) is two and the LS-categories of the skeleta are one. The author also constructs 1-connected finite type CW-complexes \(X\), \(Y\) in the same genus such that \(\text{cat }X= 2\) and \(\text{cat }Y= 1\).
Mathematics Subject Classification ID: 55M30
zbMATH DE Number: 1356312
zbMATH Keywords: Lyusternik-Shnirel'man category
zbMATH Keywords: games
zbMATH Keywords: homotopy colimit
reviewed by: Yves Félix
MaRDI profile type: Publication
full work available at URL: s0040-9383(98)00060-3
OpenAlex ID: W2033163800
description: scientific article; zbMATH DE number 1356312