Homotopy minimal periods for nilmanifold maps

Abstract.

A natural number m is called the homotopy minimal period of a map $f: X \to X$ if it is a minimal period for every map g homotopic to f. In this paper we show that the complete description of the sets of homotopy minimal periods of a torus map given by Jiang and Llibre extends to the case of a map of compact nilmanifold. The proof follows the approach of Jiang and Llibre and uses the Nielsen theory. The main geometric ingredient is a theorem on cancelling m-periodic points of a local homeomorphism. For a map of nilmanifold the general case reduces to it by a homotopy argument.