Holonomy-nilpotent fibrations and rational Lusternik-Schnirelmann category
type: Item
instance of: scholarly article
title: Holonomy-nilpotent fibrations and rational Lusternik-Schnirelmann category
zbMATH Open document ID: 0851.55016
DOI: 10.1016/0040-9383(94)00054-9
author: Barry Jessup
published in: Topology
publication date: 1996-11-24T00:00:00Z
review text: An interesting relation between the category of the total space and the category of the fibre for ``almost trivial'' fibrations \(F \overset {J} {} {E} B\) is proved. More precisely, suppose that \(\pi_*(J) \otimes \mathbb{Q}\) is injective and that some primitive element \(h \in H_{\text{even}} (\Omega B;\mathbb{Q})\) acts locally nilpotent in \(H_*(F)\) for the holonomy operation, then \(\text{cat}_0(E) \geq \text{cat}_0(F) + 1\). Here \(\text{cat}_0\) means rational category, i.e. category of the rationalization. A generalization is also given when finitely many linearly independent primitive elements of \(H_{\text{even}} (\Omega B; \mathbb{Q})\) act locally nilpotently on \(H_*(F; \mathbb{Q})\).
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55M30
zbMATH DE Number: 863704
zbMATH Keywords: rational Lyusternik-Shnirel'man category
zbMATH Keywords: holonomy representation
zbMATH Keywords: Ganea conjecture
reviewed by: Yves Félix
MaRDI profile type: Publication
full work available at URL: 0040-9383(94)00054-9
OpenAlex ID: W1986984745
description: scientific article; zbMATH DE number 863704