Some aspects of topological dynamics of Polish groups (with an introduction to descriptive set theory)

Julien Melleray

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arXiv · 2602.23799

Some aspects of topological dynamics of Polish groups (with an introduction to descriptive set theory)

Julien Melleray

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Abstract

The first part of these notes give an introduction to the theory of Polish group actions on compact Hausdorff spaces, leading up to a proof of the Kechris-Pestov-Todorcevic correspondence and discussions of properties of universal minimal flows. The second part proveides some background on descriptive set theory and culminates with B. Miller's proof of the $\mathcal{G}_0$-dichotomy theorem due to Kechris, Solecki, and Todorcevic.

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Julien Melleray. 2026-02-27. Some aspects of topological dynamics of Polish groups (with an introduction to descriptive set theory). https://arxiv.org/abs/2602.23799

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