28 October 2009
Much of group theory is concerned with whether one property entails another. When such a question is answered in the negative it is often via a pathological example. We will examine the Rips construction, an important tool for producing such pathologies, and touch upon a recent refinement of the construction and some applications. In the course of this we will introduce and consider the profinite topology on a group, various separability conditions, and decidability questions in groups.