Subexponential growth and C 1 actions on one-manifolds
Résumé
Let G be a countable group with no finitely generated subgroup of exponential growth. We show that every action of G on a countable set preserving a linear (respectively, circular) order can be realised as the restriction of some action by C 1 diffeomorphisms on an interval (respectively, the circle) to an invariant subset. As a consequence, every action of G by homeomorphisms on a compact connected one-manifold can be made C 1 upon passing to a semiconjugate action. The proof is based on a functional characterisation of groups of local subexponential growth.
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