Andy Zucker
Topological groups with tractable minimal dynamics
For Polish groups, there are several interesting dividing lines in how complicated their minimal flows can be. While metrizability of the universal minimal flow is the most obvious, a theorem of Ben Yaacov, Melleray, and Tsankov suggests the broader class of Polish groups whose universal minimal flows have a comeager orbit. In joint work with Gianluca Basso, we find natural extensions of these classes to general topological groups, obtaining the classes of topological groups with ``concrete minimal dynamics'' or ``tractable minimal dynamics,'' respectively. Both classes admit a wide variety of non-trivial characterizations. In particular, the class of groups with tractable minimal dynamics is the largest class of topological groups admitting any form of KPT correspondence, allowing us to show that this class is absolute between models of set theory.
MC 5479