Logic Seminar

Please note that the time is PST

Consider an action of a discrete group G on a compact, 0-dimensional space X. Its clopen type semigroup is an algebraic structure which encodes the equidecomposability relation between clopen subsets of X (two clopen subsets A,B of X are equidecomposable if there is a clopen partition A1,…,An of A and elements g1,…,gn of G such that g1A1,…,gnAn form a partition of B). I will discuss how some properties of the action can be studied via the clopen type semigroup; I will focus in particular on the dynamical comparison property (following Kerr and Ma), and the existence of a dense locally finite group in the topological full group associated to the action. I will also try to outline some consequences for generic properties of minimal actions of a given countable group on the Cantor space, and discuss some open problems.