Coincidence points of fiber maps on \(S^n\)-bundles
type: Item
instance of: scholarly article
title: Coincidence points of fiber maps on \(S^n\)-bundles
zbMATH Open document ID: 1196.55001
published in: Topology and its Applications
publication date: 2010-06-09T00:00:00Z
review text: The authors study coincidences for fiber-preserving maps between \(S^n\)-bundles. If \(E\to B\) is an \(S^n\)-bundle they first show the existence of a fiber-preserving map \(\tau:E\to E\) which is fixed point free and such that the degree of \(\tau|\,S^n\) is 1 if \(n\) is odd and \(-1\) if \(n\) is even. They then obtain the following result: Let \(E_1\to B\) and \(E_2\to B\) be \(S^n\)-bundles and \(f:E_1\to E_2\) a fiber-preserving map. Then there is a unique homotopy class of maps given by \(\mathcal{C}=[\tau\circ f]\) such that for \(g\in\mathcal{C}(f)\) the pair \((f,g)\) can be deformed over \(B\) to a coincidence free pair. The authors then study the case of \(S^n\)-bundles over \(S^1\).
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 55R10
zbMATH DE Number: 5718376
zbMATH Keywords: fixed point
zbMATH Keywords: fiber bundle
zbMATH Keywords: fiberwise homotopy
zbMATH Keywords: coincidence theory
zbMATH Keywords: spherical bundle
author: Daciberg Lima Gonçalves
author: D. Penteado
author: J. P. Vieira
reviewed by: Christian Fenske
MaRDI profile type: Publication
full work available at URL: j.topol.2010.02.025
OpenAlex ID: W2028289046
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DOI: 10.1016/J.TOPOL.2010.02.025
description: scientific article; zbMATH DE number 5718376