An embedding version of Rubin's theorem

Jan Gundelach

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arXiv · 2602.18197

An embedding version of Rubin's theorem

Jan Gundelach

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Abstract

Rubin's theorem asserts that if $\Gamma\curvearrowright X$ and $\Delta\curvearrowright Y$ are Rubin actions, then any group isomorphism $\Gamma \cong \Delta$ induces an equivariant homeomorphism $Y\cong X$. We provide an embedding version of Rubin's theorem highlighting group embeddings that induce a spatial equivariant map of a certain form. We further showcase instances of such embeddings between generalized Brin-Thompson groups.

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Jan Gundelach. 2026-02-20. An embedding version of Rubin's theorem. https://arxiv.org/abs/2602.18197

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