Hyperbolic automorphisms and Anosov diffeomorphisms on nilmanifolds (Q2719051)

The author investigates the following problem: On which nilmanifolds does there exist an Anosov diffeomorphism? In fact, the author gives a necessary and sufficient condition, for a nilmanifold covered by some nilpotent Lie group, to admit an Anosov diffeomorphism. For the proof he considers polynomial permutations of \(\mathbb{Q}^k\) and proves a certain embedding theorem. Finally, the author gives concrete examples of nilmanifolds on which there is no Anosov diffeomorphism.