Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds. II
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.
scientific article; zbMATH DE number 1507100