Orbit equivalence and topological conjugacy of affine actions on compact abelian groups

TL;DR

This paper investigates the rigidity and classification of affine actions on compact abelian groups, focusing on orbit equivalence and topological conjugacy, providing new insights into their structural properties.

Contribution

It introduces a classification framework for affine actions on compact abelian groups, emphasizing orbit equivalence and topological conjugacy, advancing understanding of their rigidity.

Findings

Classification of one-parameter flows of translations up to orbit equivalence

Classification of discrete group actions by translations up to topological conjugacy

Results on topological rigidity of affine actions

Abstract

In this paper we study topological rigidity of affine actions on compact connected metrizable abelian groups. We also classify one-parameter flows of translations upto orbit equivalence and discrete group actions by translations upto topological conjugacy.