The category of nilmanifolds
type: Item
instance of: scholarly article
title: The category of nilmanifolds
zbMATH Open document ID: 0755.55004
published in: L'Enseignement Mathématique. 2e Série
publication date: 1993-01-16T00:00:00Z
review text: The author uses the techniques of rational homotopy theory to prove that for a nilmanifold \(M\), we have: \(\dim M=\text{rank}(\pi_ 1(M))=\text{cat}(M)=e_ 0(M)\). Here \(e_ 0(M)\) is the invariant introduced by Toomer and defined as the largest integer \(p\) such that \(E^{p,*}_ \infty\neq 0\) in the Moore spectral sequence: \(\text{Tor}_{H^*(\Omega M;\mathbb{Q})}(\mathbb{Q},\mathbb{Q})\to H^*(M;\mathbb{Q})\).
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 57N65
zbMATH DE Number: 90889
zbMATH Keywords: Lusternik-Schnirelmann category
zbMATH Keywords: rational homotopy theory
zbMATH Keywords: nilmanifold
zbMATH Keywords: Moore spectral sequence
author: John Oprea
reviewed by: Yves Félix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 90889