K-theoretic duality for shifts of finite type

TL;DR

This paper establishes a K-theoretic duality for C*-algebras associated with subshifts of finite type, providing explicit constructions on the full Fock space that extend to a broader non-commutative duality framework.

Contribution

It proves a non-commutative Spanier-Whitehead duality for C*-algebras linked to hyperbolic homeomorphisms, specifically for subshifts of finite type, with explicit Fock space constructions.

Findings

Proves K-theoretic duality for subshifts of finite type

Provides explicit Fock space-based constructions

Extends duality concepts to hyperbolic dynamical systems

Abstract

C*-algebras generalizing Cuntz-Krieger algebras can be associated to hyperbolic homeomorphisms of compact metric spaces. They satisfy a non-commutative form of Spanier-Whitehead duality with respect to K-theory. We prove this for the case of subshifts of finite type. The special feature of the present situation is that the constructions are all done on the full Fock space and are very explicit, while the general theorem requires much more abstract machinery.