Monday September 29th, 13:00, CRM Small room
Speaker: Francesco Matucci, CRM
Title: Centralizers in R. Thompson's groups
Abstract: R. Thompson's groups F, T and V are countable groups whose elements can be represented as homeomorphisms of a real interval, of the circle, and of the Cantor set, respectively. Elements of the groups can be represented both from a dynamical point of view and from a combinatorial one, using suitable types of diagrams. We give a classification of centralizers of elements in these groups.
We achieve this by using techniques derived from the available solutions of the conjugacy problem. Using the piecewise-linear perspective one can derive centralizers in F by observing the bumps of a map. This description can be "lifted" to centralizers in T, up to finite index. The case of V is treated using the point of view of tree diagrams and choosing a suitable representative that describes the action on the underlying Cantor set by looking at the diagram. We give combinatorial and topological applications of this description.
