Nielsen type numbers for periodic points of fibre preserving maps
type: Item
instance of: scholarly article
title: Nielsen type numbers for periodic points of fibre preserving maps
zbMATH Open document ID: 1402.55001
author: Changbok Li
author: Yujin Paek
published in: Topology and its Applications
publication date: 2018-10-02T00:00:00Z
review text: Let \(p:E\to B\) be a fibration of compact ANR's, and let \(f:E\to E\) be a fibre preserving map, i.e., a map for which there exists a map \(\bar{f}:B\to B\) with \(pf=\bar{f}p\). In this paper the authors define two new Nielsen type numbers that will provide lower bounds for the minimum numbers of periodic points of period exactly \(n\) of maps \(g\) that are fibrewise homotopic to \(f\), and for the minimum numbers of periodic points of all periods dividing \(n\) of maps \(g\) that are fibrewise homotopic to \(f\). Also, some calculations and examples are given.
reviewed by: J. P. Vieira
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 55R05
zbMATH DE Number: 6946130
zbMATH Keywords: Nielsen type numbers
zbMATH Keywords: periodic points
zbMATH Keywords: fiber spaces
MaRDI profile type: Publication
full work available at URL: j.topol.2018.07.003
OpenAlex ID: W2887632548
cites work: The Nielsen numbers of maps of nil-manifolds
cites work: Q5619504
cites work: The Nielsen number of a fibre map
cites work: Nielsen Numbers of Maps of Tori
cites work: Corrections to ''The Nielsen number of a fibre map''
cites work: Fixed points of \(S^ 1\)-fibrations
cites work: Product formulae for Nielsen numbers of fibre maps
cites work: A Nielsen type number for fibre preserving maps
cites work: Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. I
cites work: Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. II
cites work: Addition formulae for Nielsen numbers and for Nielsen type numbers of fibre preserving maps
cites work: Q3031626
cites work: Nielsen type numbers for periodic points on nonconnected spaces
cites work: Nielsen type numbers for periodic points on pairs of spaces
cites work: Nielsen-type numbers for periodic points. II
cites work: Lectures on Nielsen fixed point theory
cites work: Nielsen numbers and Lefschetz numbers on solvmanifolds
cites work: A relative Nielsen number
Wikidata QID: Q129391538
DOI: 10.1016/J.TOPOL.2018.07.003
description: scientific article; zbMATH DE number 6946130