On manifolds supporting quasi Anosov diffeomorphisms

Abstract

Let $M$ be an $n$-dimensional manifold supporting a quasi Anosov diffeomorphism. If $n=3$ then either $M={\mathbb{T}}^3$, in which case the diffeomorphisms is Anosov, or else its fundamental group contains a copy of ${\mathbb{Z}}^6$. If $n=4$ then ${\Pi }_1(M)$ contains a copy of ${\mathbb{Z}}^4$, provided that the diffeomorphism is not Anosov.

5 pages