K-Theoretic Duality for Hyperbolic Dynamical Systems

TL;DR

This paper establishes a K-theoretic duality for Ruelle algebras linked to hyperbolic dynamical systems, extending previous results from shifts of finite type to more general Smale spaces, with implications for the Baum-Connes conjecture.

Contribution

It generalizes K-theoretic duality from shifts of finite type to irreducible Smale spaces, broadening the scope of noncommutative duality in dynamical systems.

Findings

K-theoretic duality holds for Ruelle algebras of irreducible Smale spaces

Connections to Baum-Connes conjecture are discussed

Implications for noncommutative geometry and dynamical systems

Abstract

The K-theoretic analog of Spanier-Whitehead duality for noncommutative C*-algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces. This had previously been proved only for shifts of finite type. Implications of this result as well as relations to the Baum-Connes conjecture and other topics are also considered.