Even Kakutani equivalence via α and β equivalence in Z²

Kyewon Koh Park and Ayşe A. Şahin

Vol. 201 (2001), No. 1, 205–221

DOI: 10.2140/pjm.2001.201.205

Abstract

We show that an even Kakutani equivalence class of ℤ² actions is “spanned” by α and β equivalence classes where α = {1 + α₁,1 + α₂}, β = {1 + β₁,1 + β₂} and {1,α_i⁻¹,β_i⁻¹} are rationally independent for i = 1,2. Namely, given such vectors α and β and two evenly Kakutani equivalent ℤ² actions S and T, we show that U is α -equivalent to S and β -equivalent to T.

Milestones

Received: 10 May 1999

Revised: 12 April 2000

Published: 1 November 2001