Work

Subexponential Growth and C1 Actions on One-Manifolds

Year: 2025

Type: article

Abstract: 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 semi-conjugate action. The proof is based on a functional characterisation of groups of local subexponential growth.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf202

Authors: Sang-hyun Kim, Mikael de la Salle, Nicolás Matte Bon, Michele Triestino