London Algebra Colloquium abstract

Distortion in Groups

Jarek Kedra (Aberdeen), 16th February 2012

Abstract

Let Ψ : H → G be a group homomorphism. If Ψ(h) is undistorted in G then h is undistorted in H. This trivial fact has obvious applications in investigating properties of homomorphisms of groups. I will introduce the notion of distortion in groups and discuss examples. For example, it is well-known that lattices in semisimple Lie groups of higher rank have many distorted elements. I will show that homeomorphisms of a compact manifold are very often undistorted. This gives restrictions on possible group actions which I will discuss.