Volume 10, issue 3 (2010)

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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
Publication
Accepted: 29 April 2010
Published: 21 July 2010
Authors
 Christopher F Novak Department of Mathematics and Statistics The University of Michigan-Dearborn 4901 Evergreen Road Dearborn, MI 48128 USA http://www-personal.umd.umich.edu/~cfnovak/Site/Homepage.html