Étale groupoids arising from products of shifts of finite type

Abstract

Two conjectures about homology groups, K-groups and topological full groups of minimal étale groupoids on Cantor sets are formulated. We verify these conjectures for many examples of étale groupoids including products of étale groupoids arising from one-sided shifts of finite type. Furthermore, we completely determine when these product groupoids are mutually isomorphic. Also, the abelianization of their topological full groups is computed. They are viewed as generalizations of the higher dimensional Thompson groups.