Geodesic
Free groups of interval exchange transformations are rare
François Dahmani1 ; Koji Fujiwara2 ; Vincent Guirardel3
1Université de Grenoble I, Saint-Martin-D'hères, France
2Kyoto University, Japan
3Université de Rennes 1, Rennes, France
Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 883-910

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DOI

We study the group IET of all interval exchange transformations. Our first main result is that the group generated by a generic pairs of elements of IET is not free (assuming a suitable irreducibility condition on the underlying permutation). Then we prove that any connected Lie group isomorphic to a subgroup of IET is abelian.
DOI : 10.4171/ggd/209
Classification : 20-XX, 37-XX
Mots-clés : Groups of diffeomorphisms, interval exchange transformation, Lie groups, free groups

François Dahmani  1   ; Koji Fujiwara  2   ; Vincent Guirardel  3

1 Université de Grenoble I, Saint-Martin-D'hères, France
2 Kyoto University, Japan
3 Université de Rennes 1, Rennes, France 
François Dahmani; Koji Fujiwara; Vincent Guirardel. Free groups of interval exchange transformations are rare. Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 883-910. doi: 10.4171/ggd/209
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     pages = {883--910},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/209/}
}
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