Quasi-factors of Minimal Flows
by
Joseph Auslander
University of Maryland

We combine two important themes in topological dynamics. These are quasi-factors, the space of closed subsets of a flow, and the Galois theory of minimal flows, which associates to every minimal flow a subgroup of the automorphism group of the universal minimal flow (the Ëllis group" of the minimal flow.)

We concentrate on "joining" quasi-factors, those obtained by representing a minimal flow on the space of closed subsets of another minimal flow. (These can also be described in terms of homomorphisms from the universal minimal flow to the two flows in question.) We determine the Ellis groups of the joining quasi-factors in a number of cases. This is accomplished using maximal highly proximal generators, which were developed by Jaap van der Woude and myself.

Date received: July 8, 1999