Locally connected Smale spaces, pinched spectrum, and infra-nilmanifolds Academic Article uri icon

abstract

  • We show that if (X, f) is a locally connected Smale space such that the local product structure on X can be lifted by a covering with virtually nilpotent group of deck transformations to a global direct product, then (X, f) is topologically conjugate to a hyperbolic infra-nilmanifold automorphism. We use this result to give a generalization to Smale spaces of a theorem of M. Brin and A. Manning on Anosov diffeomorphisms with pinched spectrum, and to show that every locally connected codimension one Smale space is topologically conjugate to a hyperbolic automorphism of a torus.

author list (cited authors)

  • Nekrashevych, V.

citation count

  • 0

publication date

  • November 2020