Kernel method for Möbius transformations and hyperbolic representations of groups

Gonzalo Emiliano Ruiz Stolowicz

Kernel method for Möbius transformations and hyperbolic representations of groups

Group Theory 2026-07-16 v1 Metric Geometry

Authors: Gonzalo Emiliano Ruiz Stolowicz

Abstract

A new kernel method is introduced for isometric actions of groups on real or complex hyperbolic spaces that allows us to classify such representations for $\mathrm{PSL}_2(\R)$ and give sufficient and necessary conditions for two such representations of any group to be conjugated.

Cite

@article{arxiv.2607.14873,
  title  = {Kernel method for Möbius transformations and hyperbolic representations of groups},
  author = {Gonzalo Emiliano Ruiz Stolowicz},
  journal= {arXiv preprint arXiv:2607.14873},
  year   = {2026}
}