Uniqueness theorem for completely non-degenerate B-groups
Complex Variables
2025-11-10 v2 Group Theory
Abstract
We prove that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are M\"obius 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.
Cite
@article{arxiv.2502.19685,
title = {Uniqueness theorem for completely non-degenerate B-groups},
author = {A. A. Glutsyuk and Yu. S. Ilyashenko},
journal= {arXiv preprint arXiv:2502.19685},
year = {2025}
}
Comments
20 pages