Continuous Interval Exchange Actions

Abstract

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

To appear in Algebraic & Geometric Topology; 16 pages, 6 figures

References in corpus (2)

• Global rigidity of solvable group actions on S^1
• A geometric classification of some solvable groups of homeomorphisms