Affable laminations

Álvaro Lozano Rojo

Affability was firstly introduced by O. Bratteli in the study of C*-algebras. AF-algebras are inductive limits of finite dimensional C*-algebras. The notion was translated to topological equivalence relations by T. Giordano, I.F. Puntnam and C.F. Skau in their seminal work "Topological orbit equivalence and C*-crossed products". Affable equivalence relations are inductive limits of compact equivalence relations over the Cantor set. One can think on affability as a topological version of hyperfiniteness. Here we want to present the main concepts about them, and show that a large class of interesting laminations introduced by É. Ghys are affable. That is part of the author PhD thesis.