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Group rings and hyperbolic geometry

Grigori Avramidi and Thomas Delzant
Geometry & Topology 30 (2026) 2337–2365
DOI: 10.2140/gt.2026.30.2337
Abstract

For a group acting on a hyperbolic space, we set up an algorithm in the group algebra showing that ideals generated by few elements are free, where few is a function of the minimal displacement of the action, and derive algebraic, geometric, and topological consequences. In particular, we obtain lower bounds on Morse complexity of closed hyperbolic manifolds in terms of injectivity radius.

Keywords
group rings, hyperbolic geometry
Mathematical Subject Classification
Primary: 20F65, 20F67
Secondary: 16D70, 20F05
References
Publication
Received: 25 October 2024
Revised: 18 November 2025
Accepted: 6 March 2026
Published: 31 July 2026
Proposed: Roman Sauer
Seconded: David Fisher, Martin R Bridson
Authors
Grigori Avramidi
Max Planck Institute for Mathematics
Bonn
Germany		 Mathematical Institute
University of Oxford
Oxford
United Kingdom
Thomas Delzant
IRMA
Université de Strasbourg & CNRS
Strasbourg
France
© 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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