The coincidence Nielsen number on non-orientable manifolds
type: Item
instance of: scholarly article
title: The coincidence Nielsen number on non-orientable manifolds
zbMATH Open document ID: 0787.55003
author: Roman Dobreńko
author: Jerzy Jezierski
published in: Rocky Mountain Journal of Mathematics
publication date: 1994-05-19T00:00:00Z
review text: This paper presents the Nielsen Theory for coincidence of maps \((f,g): M\to N\) between closed manifolds of the same dimension without assuming that \(M\) and \(N\) are orientable. This is a quite desirable theory. In order to define \(N(f,g)\) the authors work with a pair of maps \((f,g)\) which are transversal. They define some sort of local index, called semi- index which is either a positive integer or an element of \(Z_ 2\), the cyclic group of order 2. Then they develop the Nielsen theory by defining \(N(f,g)\), and they show a type of Wecken theorem. As an application they compute \(N(f,g)\) for pairs of maps \((f,g): K\to K\) where \(K\) is the Klein bottle. I shall mention that the paper [\textit{E. Fadell} and \textit{S. Husseini}, Topology 20, 53-92 (1981; Zbl 0453.55002)] gives enough evidence that in the non-orientable case the local index should be something which lies in \(Z\) or \(Z_ 2\).
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N75
zbMATH DE Number: 218633
zbMATH Keywords: index
zbMATH Keywords: transversality
zbMATH Keywords: Nielsen class
zbMATH Keywords: Wecken theorem
reviewed by: Daciberg Lima Gonçalves
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072611
OpenAlex ID: W2072001700
cites work: Nielsen Numbers of Maps of Tori
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cites work: On the generalization of the Nielsen number
cites work: The homotopy theory of coincidences
cites work: Q5557005
cites work: Differential Topology
cites work: The Nielsen product formula for coincidences
cites work: Q3940505
cites work: Lectures on Nielsen fixed point theory
cites work: Q3041986
DOI: 10.1216/RMJM/1181072611
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description: scientific article; zbMATH DE number 218633