Seminario Teoría de Grupos ICMAT-UAM

Jueves 24/1/2019, 11:30, Aula 520, UAM

Ponente: Carlos Meniño (Universidade Federal Fluminense)

Title: Locally discrete virtually free groups of real-analytic circle diffeomorphisms. Construction and classification.

Abstract: The motivotion of this work is to understand all the possible locally discrete real-analytic actions on the circle up to topological conjugacy. These actions can be subdivided in the expansive ones, already studied by B. Deroin, and non-expansive ones which are being studied by our team in different works.

In the non-expansive case, for dynamical reasons, the group is conjectured to be virtually free. We show what kind of virtually free groups do act (locally discrete and real-analytically) on the circle and we shall describe all the possible actions up to topological conjugacy. This will depend in a generalized Ping Pong lemma which characterizes algebraically the considered group.

We shall show how the generalized Ping-Pong game is defined at the level of the Bass-Serre tree associated to a presentation of the virtually free group as a graph of groups (provided by Stallings' Theorem). This Ping Pong configuration descends to the circle in a suitable partition (defined in a dynamical sort) of the circle which will be called a "Maskit partition" in analogy with Kleinian groups.

This is joint work with J. Alonso, S. Álvarez, D. Malicet and M. Triestino.