Fixed Point Theory and Applications
Volume 2006 (2006), Issue 2, Pages Article 63939, 12 p.
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
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.