Thick groups have trivial Floyd boundary

Abstract

We prove that thick groups (and more generally thick graphs) have trivial Floyd boundary. This shows a wide class of finitely generated groups that are non-relatively hyperbolic have trivial Floyd boundary. In addition to giving new examples, our result provides a common proof and framework for many of the known results in the literature.

Final prepublished version. To appear in Proceedings of the American Mathematical Society. Referee comments are incorporated in this version. In particular, the introduction now includes a more complete exposition, and the main theorem has been slightly strengthened