A measure of the deviation from there being fibrations between a pair of compact manifolds
type: Item
instance of: scholarly article
title: A measure of the deviation from there being fibrations between a pair of compact manifolds
zbMATH Open document ID: 1122.55009
author: Cornel Pintea
published in: Differential Geometry and its Applications
publication date: 2007-02-13T00:00:00Z
review text: Given two smooth manifolds \(M\) and \(N\), the \(\varphi\)-category of the pair \((M,N)\), denoted \(\varphi(M,N)\), is defined to be the minimum size of the critical set \(C(f)\) for any smooth map \(f\: M \to N\). The author notes that \(\varphi(M,N)=0\) implies that there is a submersion \(f\) which induces a fibering of \(M\) over \(N\). The homotopy sequence of the fibration then gives a relation between the homotopy groups of \(M\) and \(N\). This motivates the author's approach and he focuses on using various homotopy group constraints to obtain \(\varphi(M,N)=\infty\). The last section of the paper considers the equivariant situation.
reviewed by: John Oprea
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55N10
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 57R70
zbMATH DE Number: 5125298
zbMATH Keywords: fibration
zbMATH Keywords: category
zbMATH Keywords: critical points
MaRDI profile type: Publication
full work available at URL: j.difgeo.2006.02.002
OpenAlex ID: W1977188121
Wikidata QID: Q115357860
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DOI: 10.1016/J.DIFGEO.2006.02.002
description: scientific article; zbMATH DE number 5125298