Combination theorems for geometrically finite convergence groups

Traaseth, Alec; Weisman, Theodore

doi:10.2140/agt.2026.26.2079

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ISSN (electronic): 1472-2739

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Combination theorems for geometrically finite convergence groups

Alec Traaseth and Theodore Weisman

Algebraic & Geometric Topology 26 (2026) 2079–2122

DOI: 10.2140/agt.2026.26.2079

Abstract

We prove combination theorems in the spirit of Klein and Maskit in the context of discrete convergence groups acting geometrically finitely on their limit sets. As special cases, we obtain combination theorems for geometrically finite groups of isometries of Hadamard manifolds with pinched negative curvature, and for relatively quasiconvex subgroups of relatively hyperbolic groups.

Keywords

convergence action, convergence group, combination theorem, amalgamation

Mathematical Subject Classification

Primary: 20F65

Secondary: 57M50

References

Publication

Received: 7 February 2024

Revised: 11 April 2025

Accepted: 2 June 2025

Published: 22 June 2026

Authors

Alec Traaseth
Charlottesville, VA United States

Theodore Weisman
Department of Mathematics University of Michigan Ann Arbor, MI United States

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Volume 26, issue 6 (2026)