Homotopy minimal periods for N R-solvmanifolds maps

A natural number m is called the homotopy minimal period of a map f : X --> X if every map g homotopic to f will have periodic points of minimal period m. In this paper we give a complete description of the sets of homotopy minimal periods of a map of compact NR-solvmanifold of dimension greater than or equal to 4. In dimension 3 we are able to show this theorem for a map of completely solvable solvmanifold but the description is given as detailed listed table then. This shows that previous results for torus and compact nilmanifold extend to this case. (C) 2004 Elsevier B.V. All rights reserved.