Uniform symplicity of groups with proximal action

Abstract

We prove that groups acting boundedly and order-primitively on linear orders or acting extremly proximality on a Cantor set (the class including various Higman-Thomson groups and Neretin groups of almost automorphisms of regular trees, also called groups of spheromorphisms) are uniformly simple. Explicit bounds are provided.

23 pages, appendix by Nir Lazarovich, corrected version

References in corpus (3)

• Automorphism groups of right-angled buildings: simplicity and local splittings
• The Neretin groups
• Stable commutator length in subgroups of PL(I)

Cited by in corpus (6)

• Braided Thompson groups with and without quasimorphisms
• On spherical unitary representations of groups of spheromorphisms of Bruhat--Tits trees
• Strong and uniform boundedness of groups
• Algebraic irrational stable commutator length in finitely presented groups
• The Diophantine problem in Thompson's group F
• Metric ultraproducts of groups -- simplicity, perfectness and torsion