# On topological complexity of hyperbolic groups

## TL;DR

This paper establishes that the topological complexity of a finitely generated torsion free hyperbolic group is exactly twice its cohomological dimension, providing a precise measure of its topological intricacy.

## Contribution

It proves a exact formula linking the topological complexity and cohomological dimension for a class of hyperbolic groups, which was previously unknown.

## Key findings

- Topological complexity equals twice the cohomological dimension for these groups.
- Provides a new exact calculation method for topological complexity.
- Enhances understanding of the relationship between algebraic and topological properties of hyperbolic groups.

## Abstract

We show that the topological complexity of a finitely generated torsion free hyperbolic group $\pi$ with $\cd\pi=n$ equals $2n$.