Continuous interval exchange actions

Abstract

Let $\mathcal{ℰ}$ denote the group of all interval exchange transformations on $0\le x<1$ Given a suitable topological group structure on $\mathcal{ℰ}$, it is possible to classify all one-parameter interval exchange actions (continuous homomorphisms $ℝ\to \mathcal{ℰ}$). In particular, up to conjugacy in $\mathcal{ℰ}$, any one-parameter interval exchange action factors through a rotational torus action.