Ultracoproducts and weak containment for flows of topological groups

Abstract

We develop the theory of ultracoproducts and weak containment for flows of arbitrary topological groups. This provides a nice complement to corresponding theories for p.m.p. actions and unitary representations of locally compact groups. For the class of locally Roelcke precompact groups, the theory is especially rich, allowing us to define for certain families of $G$-flows a suitable compact space of weak types. When $G$ is locally compact, all $G$-flows belong to one such family, yielding a single compact space describing all weak types of $G$-flows.