On the Classification of Resonance-free Anosov Z~k Actions

摘要

In this paper we consider the problem of classification of higher-rank abelian Anosov actions. These are actions of Z~k and R~k, k ≥ 2, by commuting diffeomor-phisms of a compact manifold with at least one Anosov element. It is conjectured that all irreducible actions of this type are smoothly conjugate to algebraic models [10]. We will concentrate on Z~k actions. In this case, the algebraic models are actions by commuting automorphisms of tori and infranilmanifolds.