Wecken's theorem for periodic points in dimension at least 3

摘要

Boju Jiang introduced a homotopy invariant NF_n(f), for a natural number n, which is a lower bound for the cardinality of periodic points, of period n, of a self-map of a compact polyhedron. In [J. Jezierski, Wecken theorem for periodic points, Topology 42 (5) (2003) 1101-1124] and [J. Jezierski, Wecken theorem for fixed and periodic points, in: Handbook of Topological Fixed Point Theory, Kluwer Academic, Dordrecht, 2005] we prove that any self-map of a compact PL-manifold f :M → M (dim M ≥ 3) is homotopic to a map g satisfying #Fix(g~n) = NF_n(f) i.e. NF_n(f) is the best such homotopy invariant. Here we give an alternative, simpler proof of these results.