Journal of group theory vol:6 issue:3 pages:381-389
A virtually unipotent map of an n-dimensional. at Riemannian manifold M is ( up to homotopy) a diffeomorphism of M lifting to an affine transformation of the universal cover R-n whose linear part only has roots of unity as eigenvalues. Of course, a homotopically periodic map of M is always virtually unipotent. Conversely, in this paper we prove that each virtually unipotent map of M is homotopically periodic if and only if the associated rational holonomy representation is multiplicity-free. Finally, we discuss the existence of Anosov diffeomorphisms on. at Riemannian manifolds with multiplicity-free rational holonomy representation.