# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Boomerang subgroups and the Stuck-Zimmer theorem"

#### Lederle, Waltraud

We introduce the notion of boomerang subgroups of a discrete group. Those are subgroups satisfying a strong recurrence property, when we consider them as elements of the space of all subgroups with the conjugation action. We prove that every boomerang subgroup of $\mathrm{SL}_n(\mathbb{Z})$ for $n \geq 3$ is finite or of finite index. Thus we give a new proof of the Stuck-Zimmer rigidity theorem for $\mathrm{SL}_n(\mathbb{Z})$ avoiding almost all measure theory. This is joint work with Yair Glasner.

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