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Subexponential growth and $C^1$ actions on one-manifolds
- Publication Year :
- 2024
-
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.<br />Comment: 14 pages
- Subjects :
- Mathematics - Group Theory
Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2410.02614
- Document Type :
- Working Paper