Lamplighters over non-amenable groups are not strongly Ulam stable

2020/09/24 by Andrei Alpeev, Alpeev, Andrei
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2009.11738

openalex publication_date 2020/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a wreath product of an abelian group and a non-amenable group is not strongly Ulam stable. Previously this was known for groups containing free subgroups, due to work of Burger, Ozawa and Thom, and for some surface groups, due to work by Kazhdan. We also show that these wreath products are not deformation rigid.

Related

• Profinite rigidity of lamplighter groups
• Unrestricted wreath products and sofic groups
• Ulam stability of lamplighters and Thompson groups
• Proper actions of lamplighter groups associated with free groups
• The Profinite Rigidity of Torsion-Free Lamplighter Groups