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arXiv · 1907.13204

Simplicity of the automorphism groups of generalised metric spaces

David M. Evans·Jan Hubička·Matěj Konečný·Yibei Li·Martin Ziegler
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Abstract

Tent and Ziegler proved that the automorphism group of the Urysohn sphere is simple and that the automorphism group of the Urysohn space is simple modulo bounded automorphisms. A key component of their proof is the definition of a stationary independence relation (SIR). In this paper we prove that the existence of a SIR satisfying some extra axioms is enough to prove simplicity of the automorphism group of a countable structure. The extra axioms are chosen with applications in mind, namely homogeneous structures which admit a "metric-like amalgamation", for example all primitive 3-constrained metrically homogeneous graphs of finite diameter from Cherlin's list.

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David M. Evans, Jan Hubička, Matěj Konečný, Yibei Li, Martin Ziegler. 2019-07-30. Simplicity of the automorphism groups of generalised metric spaces. https://doi.org/10.1016/j.jalgebra.2021.04.035

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