#### Volume 10, issue 3 (2010)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
Continuous interval exchange actions

### Christopher F Novak

Algebraic & Geometric Topology 10 (2010) 1609–1625
##### Abstract

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

##### Keywords
interval exchange, group action, one-parameter subgroup
##### Mathematical Subject Classification 2000
Primary: 37E05, 54H15
Secondary: 57S05, 37A10, 57M60