4 problems

Let $M$ be a closed manifold and let $f:M\to M$ be an Anosov diffeomorphism. A hyperbolic affine infra-nil-automorphism is an affine automorphism of an infra-nil-manifold whose lin…

Let $M$ be a closed manifold and let $f\colon M\to M$ be an Anosov diffeomorphism, meaning a diffeomorphism with a hyperbolic splitting of the tangent bundle. A hyperbolic infra-ni…

The non-trivial self-cover conjecture. The infra-nilmanifold $\Gamma \backslash G$ admits a non-trivial self-cover if and only if the nilmanifold $N \backslash G$ admits an expandi…

The expanding-map lifting conjecture. The infra-nilmanifold $\Gamma \backslash G$ admits an expanding map if and only if the nilmanifold $N \backslash G$ admits an expanding map.