Lamplighter groups, median spaces and Hilbertian geometry. Issue 2 (9th May 2022)

• Record Type: Journal Article
• Authors: Genevois, Anthony
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 65:Issue 2(2022)
• Page Start: 500
• Page End: 529
• Publication Date: 2022-05-09
• Subjects: Wreath products -- median spaces -- CAT(0) cube complexes -- compression -- Haagerup property -- Kazhdan property (T); 20F65 -- 20F67; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091522000190
• Languages: English
• ISSNs: 0013-0915

Abstract

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 $G\wr H \to X \circledast Y$ . The construction offers a unified point of view on various questions related to the Hilbertian geometry of wreath products of groups.