Dynamics of isolated orders

Abstract

We study some properties of the dynamical realization of isolated left orders of a countable group G. We show that the dynamical realization admits a unique minimal set provided G is not infinite cyclic. We show that convex subgroup of an isolated left order is finite in number. Using this, we give a dynamical proof of the Tararin theorem. We also show that there is a new isolated order on the braid group B_3.