Fixed points on null and tame flows for groups of automorphisms

Alessandro Codenotti

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arXiv · 2507.12239

Fixed points on null and tame flows for groups of automorphisms

Alessandro Codenotti

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Abstract

Using a generalization of the Kechris-Pestov-Todor\v{c}evi\'{c} correspondence due to Nguyen Van Th\'{e} we obtain fixed point theorems for null and tame actions of groups of the form $\mathrm{Aut}(\mathcal F)$, where $\mathcal{F}$ is a Fra\"{i}ss\'{e} structure. In particular we show that if $\mathrm{Age}(\mathcal F)$ is a free joint embedding class, then every null flow $\mathrm{Aut}(\mathcal F)\curvearrowright X$ has a fixed point, while if $\mathrm{Age}(\mathcal F)$ is a free amalgamation class, then every tame flow $\mathrm{Aut}(\mathcal F)\curvearrowright X$ has a fixed point.

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BibTeX RIS

Alessandro Codenotti. 2025-07-16. Fixed points on null and tame flows for groups of automorphisms. https://arxiv.org/abs/2507.12239

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