Open Access

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

Fixed Point Theory and Applications20062006:63939

DOI: 10.1155/FPTA/2006/63939

Received: 9 September 2004

Accepted: 21 July 2005

Published: 8 March 2006


We prove that for any continuous map 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.


Authors’ Affiliations

Department of Mathematics, Katholieke Universiteit Leuven Campus Kortrijk


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© K. Dekimpe et al. 2006

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