Nicolas Matte Bon [1]
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. We will see 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 we
will investigate the structure of such actions. This is joint work
with Joaquín Brum, Cristóbal Rivas and Michele Triestino.