Abstract
AbstractWe show that a large family of groups is uniformly stable relative to unitary groups equipped with submultiplicative norms, such as the operator, Frobenius, and Schattenp-norms. These include lamplighters$$\Gamma \wr \Lambda $$Γ≀Λwhere$$\Lambda $$Λis infinite and amenable, as well as several groups of dynamical origin such as the classical Thompson groups$$F, F', T$$F,F′,TandV. We prove this by means of vanishing results in asymptotic cohomology, a theory introduced by the second author, Glebsky, Lubotzky and Monod, which is suitable for studying uniform stability. Along the way, we prove some foundational results in asymptotic cohomology, and use them to prove some hereditary features of Ulam stability. We further discuss metric approximation properties of such groups, taking values in unitary or symmetric groups.
Funder
Swiss Federal Institute of Technology Zurich
Publisher
Springer Science and Business Media LLC
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