Hierarchies for Relatively Hyperbolic Virtually Special Groups
Group Theory
2025-11-26 v3 Geometric Topology
Abstract
Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we construct a new virtual quasiconvex hierarchy for relatively hyperbolic virtually compact special groups. We use this hierarchy to prove a generalization of Wise's Malnormal Special Quotient Theorem for relatively hyperbolic virtually compact special groups with arbitrary peripheral subgroups.
Cite
@article{arxiv.1903.12284,
title = {Hierarchies for Relatively Hyperbolic Virtually Special Groups},
author = {Eduard Einstein},
journal= {arXiv preprint arXiv:1903.12284},
year = {2025}
}
Comments
Extensively revised version accepted for publication in Algebraic and Geometric Topology