Flocks in topological circle planes and their representation in generalised quadrangles

Abstract In this paper we prove that there is a flock in every locally compact 2-dimensional Laguerre plane, i.e., a set of disjoint circles which covers the point space. We then determine the homeomorphism type of these flocks and use the relation between circle planes and generalised quadrangles to obtain analogous results about generalised quadrangles, Möbius planes and Minkowski planes.