On manifolds supporting quasi-Anosov diffeomorphisms

Let M be an n-dimensional manifold supporting a quasi-Anosov diffeomorphism. If n = 3 then either M = T-3, in which case the diffeomorphisms is Anosov. or else its fundamental group contains a copy of Z(6). If n = 4 then Pi(1) (M) contains a copy of Z(4). provided that the diffeomorphism is not Anosov. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.