Subgroups of interval exchange transformations

An interval exchange transformation (IET) is a bijective map f :I = [0, 1) → [0, 1) defined by a finite partition of I into half-open subintervals and a reordering of these intervals by translations. We denote by IET the group consisting in all IETs.

The IETs have been a very popular subject of study in ergodic theory: most papers on IETs concern specific dynamical and spectral properties (minimality, ergodicity, mixing properties ...) of a single map.

In this talk, I will address certain questions on the group-theoretical structure of IET and the question I will focus on is what abstract groups can be represented as subgroups of IET.

I will discuss examples and properties of certain subgroups in IET. This is a joint work with Nancy Guelman.