Group rings and hyperbolic geometry
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Geometry & Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 30
- Issue
- 6
- Pages
- 2337–2365
- Publication date
- 31 July 2026
- Language
- EN