Work

Finite index rigidity of hyperbolic groups

Year: 2025

Type: article

Abstract: We prove that the topological complexity of a finite index subgroup of a hyperbolic group is linear in its index. This follows from a more general result relating the size of the quotient of a free cocompact action of a hyperbolic group on a graph to the minimal number of cells in a simplicial classifying space for the group. As a corollary, we prove that any two isomorphic finite index subgroups of a non-elementary hyperbolic group have the same index.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1618

Author: Nir Lazarovich

Institution: Technion – Israel Institute of Technology

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408525374

FWCI: 1.802

Cites:

Cited by: 1

Related to: 10