Coincidences in codimension one
type: Item
instance of: scholarly article
title: Coincidences in codimension one
zbMATH Open document ID: 1404.55003
author: Ulrich Koschorke
author: Gustavo de Lima Prado
published in: Journal of Fixed Point Theory and Applications
publication date: 2018-07-18T00:00:00Z
review text: Let \((f_{1},f_{2})\) be a pair of maps from the \((n+1)\)-sphere \(S^{n+1}\) to a manifold \(Y\) of dimension \(n \geq 1.\) In this paper the authors study the minimum numbers \(MC(f_{1}, f_{2})\) and \(MCC(f_{1},f_{2}),\) where \[ MC(f_{1},f_{2}):= \min\{\#\mathrm{Coin}(f^{'}_{1},f^{'}_{2})\mid (f^{'}_{1},f^{'}_{2}) \simeq (f_{1},f_{2}) \} \] and \[ MCC(f_{1},f_{2}):= \min\{\#\pi_{0}(\mathrm{Coin}(f^{'}_{1},f^{'}_{2}))\mid (f^{'}_{1},f^{'}_{2}) \simeq (f_{1},f_{2}) \} \] The study of these sets is based on the so-called \(\omega\)-invariant which is defined using framed bordism. Computations of \(MC(f_{1}, f_{2})\) and \(MCC(f_{1},f_{2}),\) in the case of \(Y = \mathbb{C}P(n), \,\, n \geq 1\) or \(Y = S^{n}/G ,\) the orbit manifold of a finite group \(G\) acting freely and smoothly on the \(n\)-sphere, \(n \geq 3,\) are presented. The authors also present a type of Wecken theorem for coincidence, the proof is in terms of the \(\omega\)-invariant.
reviewed by: Weslem L. Silva
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 55N22
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 55Q05
zbMATH DE Number: 6905246
zbMATH Keywords: coincidences
zbMATH Keywords: codimension one
MaRDI profile type: Publication
full work available at URL: s11784-018-0533-6
OpenAlex ID: W2792978532
cites work: Q4278134
cites work: Q5557005
cites work: One codimensional Wecken type theorems
cites work: Commutativity and Wecken properties for fixed points on surfaces and 3- manifolds
cites work: Nielsen coincidence theory in arbitrary codimensions
cites work: Nonstabilized Nielsen coincidence invariants and Hopf-Ganea homomorphisms
cites work: Selfcoincidences and roots in Nielsen theory
cites work: Q5387285
cites work: Minimum numbers and Wecken theorems in topological coincidence theory. I
cites work: Nielsen coincidence numbers, Hopf invariants and spherical space forms
cites work: Q5757489
Wikidata QID: Q130156428
DOI: 10.1007/S11784-018-0533-6
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description: scientific article; zbMATH DE number 6905246