Characterizations of contracting Hurwitz bisets
Abstract
A critically finite branched self-cover $f: (S^2, P) \to (S^2, P)$ determines naturally three iterated function systems: one on the pure mapping class group of the sphere marked at $P$, one on the Teichmüller space of the sphere marked at $P$, and one on a finite-dimensional real vector space. We show that contraction for any one of these systems implies contraction for the others.
Fields of Study & Subjects
Holomorphic and Operator Theory
Analytic and geometric function theory
Geometric and Algebraic Topology
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Publication date
- 11 April 2026
- Language
- EN