Uniqueness theorem for completely non-degenerate $B$-groups
Abstract
We show that a completely non-degenerate $B$-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Möbius conjugate. A similar property is inherent to the quasi-Fuchsian groups but not to degenerate $B$-groups. We also study the factor of a $B$-group as a triple: the main factor, the marked characteristic complex, and a homotopy class of maps of the first to the second one.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Advanced Algebra and Geometry
Publication details
- Journal / source
- Известия Российской академии наук Серия математическая
- Volume
- 90
- Issue
- 1
- Pages
- 73–89
- Publication date
- 1 January 2026
- Language
- RU