4 papers
On quantitative orbit equivalence for lamplighter-like groups
Corentin Correia, Vincent Dumoncel
We focus on halo products, a class of groups introduced by Genevois and Tessera, and whose geometry mimics lamplighters. Famous examples are lampshufflers. Motivated by their work…
Isoperimetric profiles of lamplighter-like groups
Corentin Correia, Vincent Dumoncel
Given a finitely generated amenable group satisfying some mild assumptions, we relate isoperimetric profiles of the lampshuffler group $\mathsf{Shuffler}(H)=\mathsf{FSym}(H)\rt…
Quasi-isometric rigidity for lamplighters with lamps of polynomial growth
Vincent Dumoncel
A quasi-isometry between two connected graphs is measure-scaling if one can control precisely the sizes of pre-images of finite subsets. Such a notion is motivated by the work of E…
On the quasi-isometric classification of permutational wreath products
Vincent Dumoncel
In this article, we initiate the study of the large-scale geometry of permutational wreath products of the form , where is finitely presented and where is a no…