Projectivity in topological dynamics

Jashan Bal

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arXiv · 2511.14944

Projectivity in topological dynamics

Jashan Bal

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Abstract

We study projectivity in the category of $G$-flows and affine $G$-flows for Polish groups $G$. We also introduce the notion of \emph{proximally irreducible} extensions between affine $G$-flows. Using this we provide a characterization of extreme amenability, strong amenability, and amenability for closed subgroups $H \leq G$ in terms of certain ``dynamical irreducibility'' properties of the Samuel compactification of $G/H$. We then apply this to answer an open question of Zucker by proving a structure theorem for when the universal minimal proximal flow of $G$ is metrizable or contains a comeager orbit.

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Jashan Bal. 2025-11-18. Projectivity in topological dynamics. https://arxiv.org/abs/2511.14944

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