Hierarchies for relatively hyperbolic virtually special groups

Einstein, Eduard

doi:10.2140/agt.2025.25.4437

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Hierarchies for relatively hyperbolic virtually special groups

Eduard Einstein

Algebraic & Geometric Topology 25 (2025) 4437–4497

DOI: 10.2140/agt.2025.25.4437

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.

Keywords

hierarchies for relatively hyperbolic groups, virtually special relatively hyperbolic groups, $\mathrm{CAT}(0)$ cube complexes

Mathematical Subject Classification 2010

Primary: 20F65, 20F67

References

Publication

Received: 9 October 2019

Revised: 6 August 2024

Accepted: 14 October 2024

Published: 20 November 2025

Authors

Eduard Einstein
Department of Mathematics and Statistics Swarthmore College Swarthmore, PA United States

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Volume 25, issue 8 (2025)