Weckenʹs theorem for periodic points in dimension at least 3

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.