TMD is a new class of topological groups with tractable minimal dynamics, characterized by several equivalent conditions, equal to GPP on Polish groups, admitting an abstract KPT correspondence, and yielding a forcing-based proof of the revised Newelski conjecture for all definable NIP groups.
Ultracoproducts and weak containment for flows of topological groups
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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.
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Topological groups with tractable minimal dynamics
TMD is a new class of topological groups with tractable minimal dynamics, characterized by several equivalent conditions, equal to GPP on Polish groups, admitting an abstract KPT correspondence, and yielding a forcing-based proof of the revised Newelski conjecture for all definable NIP groups.