Higher finiteness properties of braided groups

Abstract

The properties of a group to be finitely generated or finitely presentable are the first two instances in a sequence of so called higher finiteness properties defined in terms of skeletons of classifying spaces. The study of higher finiteness properties is a prime example of how one can use a nice action of a group on a topological space to better understand the group. We shall illustrate this method in detail using the braided Thompson group $V^{\mathrm{br}}$ as an example.