Introduction to Small Cancellation Groups

Over the past few years, small cancellation theory has become an important topic in discrete group theory. In light of recent breakthroughs in the field, it seems more and more likely to become essential knowledge for all potential group theorists. In this talk, I will present the foundations of geometric group theory, and explain how small cancellation groups arise naturally from the basics. Then, I will present basic properties and tools of the theory of small cancellation groups, such as Greendlinger’s Lemma and Rips’ short-exact sequence. I will conclude by providing a few comments on the role of these groups in the greater scheme of things.