K-Theoretic Duality for Hyperbolic 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.

36 pages

References in corpus (2)

• Noncommutative Poincare duality for boundary actions of hyperbolic groups
• K-theoretic duality for shifts of finite type

Cited by in corpus (9)

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• On finitely summable Fredholm modules from Smale spaces
• A Cuntz-Pimsner Model for the $C^{\ast }$-algebra of a Graph of Groups
• A geometric representative for the fundamental class in KK-duality of Smale spaces
• Homology and K-theory of dynamical systems III. Beyond stably disconnected Smale spaces
• Spanier-Whitehead K-Duality and Duality of Extensions of $C^{\ast }$-algebras