Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. II
type: Item
instance of: scholarly article
title: Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. II
zbMATH Open document ID: 0953.55001
DOI: 10.1016/S0166-8641(99)00079-6
author: Philip R. Heath
author: Edward C. Keppelmann
published in: Topology and its Applications
publication date: 2001-01-23T00:00:00Z
review text: The Nielsen periodic number \(NP_n(f)\) of a mapping \(f:X\to X\) is defined as the minimal number of periodic points of period exactly \(n\) for all mappings \(f'\) homotopic to \(f\). In the first paper [ibid. 76, No. 3, 217-247 (1997; Zbl 0881.55002)] the authors showed how to compute this number (and a similarly defined number \(N\Phi_n(f)\)) for mappings which satisfy a special property (of being weakly Jiang). In this paper, an addition property is described which enables us to compute \(NP_n(f)\) and \(N\Phi_n(f)\) for non-weakly Jiang fiber-preserving mappings. Among other examples, the authors compute the Nielsen numbers for a self-mapping of the Klein bottle.
Mathematics Subject Classification ID: 55M20
zbMATH DE Number: 1507100
zbMATH Keywords: Nielsen numbers
zbMATH Keywords: periodic points
zbMATH Keywords: nilmanifolds
zbMATH Keywords: weakly Jiang mapping
reviewed by: Olga Kosheleva
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1507100