Type invariants for non-abelian odometers

Ergodic Theory and Dynamical Systems, vol. 46, pp. 182–210

Abstract

Abstract In this work, we introduce the type and typeset invariants for equicontinuous group actions on Cantor sets; that is, for generalized odometers. These invariants are collections of equivalence classes of asymptotic Steinitz numbers associated to the action. We show the type is an invariant of the return equivalence class of the action. We introduce the notion of commensurable typesets and show that two actions which are return equivalent have commensurable typesets. Examples are given to illustrate the properties of the type and typeset invariants. The type and typeset invariants are used to define homeomorphism invariants for solenoidal manifolds.

Authors 2

1. Steven Hurder corresponding

   University of Illinois Chicago

   Affiliation as printed

   University of Illinois at Chicago

2. Olga Lukina Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University