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Commutator group of the group of interval exchange transformations

4:00 pm Thursday, October 20, 2011
Yaroslav Vorobets (Texas A&M)

An interval exchange transformation is a simple transformation of an interval: one cuts the interval into finitely many subintervals and then rearranges them by translation. The interval exchanges have been popular objects of study in ergodic theory. However this talk is concerned with group-theoretical properties of the transformation group they form.

I am going to discuss several characterizations of the commutator group of the group of interval exchange transformations. In particular, it turns out that the commutator group is generated by elements of order 2.

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