Combinations and chromatography of paths of Kleinian groups

Matthew Zevenbergen

Combinations and chromatography of paths of Kleinian groups

Geometric Topology 2026-07-15 v1

Authors: Matthew Zevenbergen

Abstract

We study continuous paths in the Chabauty topology on the set $\mathcal{D}_n$ of torsion free discrete subgroups of the isometry group of $n$ -dimensional hyperbolic space. We prove a combination theorem for paths in $\mathcal{D}_n$ , which allows us to construct an exotic path of discrete subgroups along which no two subgroups are isomorphic. We also introduce a technique we refer to as "chromatography" to prove a decomposition theorem that characterizes paths of convex cocompact groups in $\mathcal{D}_3$ .

Keywords

Kleinian groups Chabauty topology combination theorem convex cocompact groups decomposition theorem hyperbolic space

Cite

@article{arxiv.2607.13950,
  title  = {Combinations and chromatography of paths of Kleinian groups},
  author = {Matthew Zevenbergen},
  journal= {arXiv preprint arXiv:2607.13950},
  year   = {2026}
}

Comments

31 pages, 3 figures. Subsection 4.2 was split from v1 of arXiv:2410.15537 and heavily revised