The rational Lusternik-Schnirelmann category of products and of Poincaré duality complexes
type: Item
instance of: scholarly article
title: The rational Lusternik-Schnirelmann category of products and of Poincaré duality complexes
zbMATH Open document ID: 0897.55001
DOI: 10.1016/S0040-9383(97)00061-X
author: Yves Félix
author: Jean-Michel Lemaire
author: Stephen Halperin
published in: Topology
publication date: 1998-10-12T00:00:00Z
review text: Let \(X\) be a simply connected CW complex having finite-dimensional rational homology in each degree. The rational LS category of \(X\) (denoted by \(\text{cat}_0X\)) is the LS category of its rationalization \(X_{\mathbb{Q}}\). In this paper, the authors show that \(\text{cat}_0X\) depends only on the structure of \(C_*(X; \mathbb{Q})\) as a module over the cochain algebra \(C^*(X; \mathbb{Q})\) and they give a homological recipe for computing \(\text{cat}_0X\). Two theorems are easily obtained from the above-mentioned result: Theorem 1: \(\text{cat}_0(X\times Y)= \text{cat}_0X+ \text{cat}_0Y\): Theorem 3: If \(X\) is a Poincaré duality complex, then \(\text{cat}_0X= e_0(X)\), where \(e_0\) is Toomer's invariant.
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 57P10
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 1133064
zbMATH Keywords: Lyusternik-Shnirel'man category
zbMATH Keywords: Toomer's invariant
reviewed by: Dorin Andrica
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1133064