Centralizers of -contractions of the half line
Christian BonattiUniversité de Bourgogne, Dijon, France
Églantine FarinelliUniversité de Bourgogne, Dijon, France
A subgroup is -close to the identity if there is a sequence such that the conjugates tend to the identity for the -topology, for every . This is equivalent to the fact that can be embedded in the -centralizer of a -contraction of (see  and Theorem 1.1).
We first describe the topological dynamics of groups -close to the identity. Then, we show that the class of groups -close to the identity is invariant under some natural dynamical and algebraic extensions. As a consequence, we can describe a large class of groups whose topological dynamics implies that they are -close to the identity.
This allows us to show that the free group admits faithful actions which are -close to the identity. In particular, the -centralizer of a -contraction may contain free groups.
Cite this article
Christian Bonatti, Églantine Farinelli, Centralizers of -contractions of the half line. Groups Geom. Dyn. 9 (2015), no. 3, pp. 831–889DOI 10.4171/GGD/330