Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Locally moving groups acting on intervals

Talk by Dr. Nicolas Matte Bon

Speaker invited by: Prof. Dr. Corinna Ulcigrai

**Date:** 29.11.21 **Time:** 15.00 - 16.00 **Room:** Y27H28

Given a group, we are interested in understanding and classifying its actions on one-dimensional manifolds, that its representations into the groups of homeomorphisms or diffeomorphisms of an interval or the circle. In this talk we will address this problem for a class of groups arising via an action on intervals of a special type, called locally moving. A well studied example in this class is the Thompson group. I will explain that if G is a locally moving group of homeomorphisms of a real interval, then every action of G on an interval by diffeomorphisms (of class C^1) is semiconjugate to the natural defining action of G. In contrast such a group can admit a much richer space of actions on intervals by homeomorphisms, and for a class of locally moving groups I will present a structure theorem for such actions. This is joint work with Joaquín Brum, Cristóbal Rivas and Michele Triestino.