Logic Seminar

Much of the current theory of orbit equivalence for minimal actions of abelian groups on the Cantor space is based on absorption theorems - roughly speaking, theorems that state that a "small" extension of a given equivalence relation is isomorphic to the original equivalence relation. I will describe a statement equivalent to the strongest known absorption theorem, which is due to Matui (building on work of Giordano, Putnam, and Skau), and try to give intuition for a relatively elementary proof of that statement by working out a particular case. In particular, I intend to explain why, if g is a minimal homeomorphism of the Cantor space, then the equivalence relation obtained by gluing two g-orbits (and leaving all other orbits unchanged) is isomorphic to the equivalence relation induced by g.