Frucht's theorem in Borel setting

Onur Bilge; Burak Kaya

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arXiv · 2205.06335

Frucht's theorem in Borel setting

Onur Bilge·Burak Kaya

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Abstract

In this paper, we show that Frucht's theorem holds in Borel setting. More specifically, we prove that any standard Borel group can be realized as the Borel automorphism group of a Borel graph. A slight modification of our construction also yields the following result in topological setting: Any Polish group can be realized as the homeomorphic automorphism group of a $\mathbf{\Delta^0_2}$-graph on a Polish space.

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BibTeX RIS

Onur Bilge, Burak Kaya. 2022-05-12. Frucht's theorem in Borel setting. https://arxiv.org/abs/2205.06335

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