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 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 GH → X Y . The construction offers a unified point of view on various questions related to the Hilbertian geometry of wreath products of groups.