Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 63939, 12 pages

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

Copyright © 2006 K. Dekimpe et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.