Resumen de Minimal dynamical systems on the product of the Cantor set and the circle II

Huaxin Lin, Hiroki Matui

• Let X be the Cantor set and ϕ be a minimal homeomorphism on X ×T. We show that the crossed product C ∗ -algebra C ∗ (X ×T, ϕ) is a simple AT-algebra provided that the associated cocycle takes its values in rotations on T. Given two minimal systems (X ×T, ϕ) and (Y ×T, ψ) such that ϕ and ψ arise from cocycles with values in isometric homeomorphisms on T, we show that two systems are approximately K-conjugate when they have the same K-theoretical information.