Locally connected Smale spaces, pinched spectrum, and infra-nilmanifolds (Q2006090)

A Smale space is a compact metrizable space \(\mathcal X\) together with a homeomorphism preserving a local product structure such that \(f\) acts as a contraction on stable leaves and as an expansion on unstable leaves. The main result of the paper is that if \((\mathcal X, f)\) is a locally connected Smale space such that the local product structure on \(\mathcal X\) can be lifted by a covering with virtually nilpotent group of deck transformations to a global direct product, then \((\mathcal X, f)\) is topologically conjugate to a hyperbolic infra-nilmanifold automorphism.