Groups, Geometry, and Dynamics


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Volume 6, Issue 4, 2012, pp. 755–763
DOI: 10.4171/GGD/173

Published online: 2012-11-10

Interval exchanges that do not occur in free groups

Christopher F. Novak[1]

(1) University of Michigan-Dearborn, USA

A disjoint rotation map is an interval exchange transformation (IET) on the unit interval that acts by rotation on a finite number of invariant subintervals. It is currently unknown whether the group $\mathcal{E}$ of all IETs possesses any non-abelian free subgroups. It is shown that it is not possible for a disjoint rotation map to occur in a subgroup of $\mathcal{E}$ that is isomorphic to a non-abelian free group.

Keywords: Interval exchange, group action

Novak Christopher: Interval exchanges that do not occur in free groups. Groups Geom. Dyn. 6 (2012), 755-763. doi: 10.4171/GGD/173