A connection between Lipschitz and Kazhdan constants for groups of homeomorphisms of the real line
Abstract
We exhibit an obstruction for groups with Relative Property (T) to act on the real line by bi-Lipschitz homeomorphisms. This condition is expressed in terms of the Lipschitz and Kazhdan constants associated to finite generating subsets. As an application, we obtain an explicit lower bound for the Lipschitz constants associated to actions of the semidirect product $\mathbb{F}_2\ltimes\mathbb{Z}^2$. We also obtain an upper bound for the Kazhdan constants of pairs of orderable groups, depending only on the cardinal of the generating subset.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Mathematical Dynamics and Fractals
Functional Equations Stability Results
Publication details
- Journal / source
- Bulletin of the Belgian Mathematical Society - Simon Stevin
- Volume
- 33
- Issue
- 1
- Publication date
- 8 March 2026
- Language
- EN