Totally disconnected locally finite groups of prescribed finiteness lengths

In this talk I will give an introduction to analogues to the classical finiteness conditions FP_n for totally disconnected locally compact groups. I will present a construction of non-discrete tdlc groups of arbitrary finiteness length. As a bi-product we also obtain a new collection of (discrete) Thompson-like groups which contains, for all positive integers n, groups of type FP_n but not of type FP_{n+1}. This is joint work with I. Castellano, B. Marchionna, and Y. Santos-Rego.