Existence of Anosov diffeomorphisms on infra-nilmanifolds modeled on free nilpotent Lie groups

Karel Dekimpe, Jonas Deré

DOI: http://dx.doi.org/10.12775/TMNA.2015.042


An infra-nilmanifold is a manifold which is constructed as a~quotient space $\Gamma\setminus G$ of a simply connected nilpotent Lie group $G$, where $\Gamma$ is a discrete group acting properly discontinuously and cocompactly on~$G$ via so called affine maps. The manifold $\Gamma\setminus G$ is said to be modeled on the Lie group~$G$. This class of manifolds is conjectured to be the only class of closed manifolds allowing an Anosov diffeomorphism. However, it is far from obvious which of these infra-nilmanifolds actually do admit an Anosov diffeomorphism. In this paper we completely solve this question for infra-nilmanifolds modeled on a free $c$-step nilpotent Lie group.


Anosov diffeomorphism; infra-nilmanifold; freenilpotent Lie group

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