Lamplighter groups, median spaces and Hilbertian geometry. Issue 2 (9th May 2022) - Genevois, Anthony
Abstract: From any two median spaces $X$ and $Y$, we construct a new median space $X \circledast Y$, referred to as the diadem product of $X$ and $Y$, and we show that this construction is compatible with wreath products in the following sense: given two finitely generated groups $G, \, H$ and two (equivariant) coarse embeddings into median spaces $X, \, Y$, there exist a(n equivariant) coarse embedding $G\wr H → X \circledast Y$ . The construction offers a unified point of view on various questions related to the Hilbertian geometry of wreath products of groups.