1 results
Lamplighter groups, median spaces and Hilbertian geometry
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 2 / May 2022
- Published online by Cambridge University Press:
- 09 June 2022, pp. 500-529
-
- Article
- Export citation
-
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.
