Fixed Point Theory and Applications 
Volume 2006 (2006), Article ID 63939, 12 pages
doi:10.1155/FPTA/2006/63939

The anosov theorem for infranilmanifolds with an odd-order abelian holonomy group

K. Dekimpe, B. De Rock, and H. Pouseele

 Department of Mathematics, Katholieke Universiteit Leuven Campus Kortrijk, Universitaire Campus, Etienne Sabbelaan 53, Kortrijk 8500, Belgium
Received 9 September 2004; Revised 18 February 2005; Accepted 21 July 2005

Abstract

We prove that N(f)=|L(f)| for any continuous map f of a given infranilmanifold with Abelian holonomy group of odd order. This theorem is the analogue of a theorem of Anosov for continuous maps on nilmanifolds. We will also show that although their fundamental groups are solvable, the infranilmanifolds we consider are in general not solvmanifolds, and hence they cannot be treated using the techniques developed for solvmanifolds.