An embedding version of Rubin's theorem

Abstract

Rubin's theorem asserts that if $\hat{I}“\curvearrowright X$ and $\hat{I}”\curvearrowright Y$ are Rubin actions, then any group isomorphism $\hat{I}“\cong \hat{I}”$ 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.

9 pages