On the topological complexity of toral relatively hyperbolic groups

TL;DR

This paper establishes a precise relationship between the topological complexity and cohomological dimension for a class of toral relatively hyperbolic groups, advancing understanding in geometric group theory.

Contribution

It proves that for certain toral relatively hyperbolic groups, the topological complexity equals the cohomological dimension of their product, a novel result in the field.

Findings

Topological complexity equals cohomological dimension for these groups.

Provides new insights into the structure of toral relatively hyperbolic groups.

Enhances understanding of the interplay between algebraic and topological properties.

Abstract

We prove that the topological complexity $\mathrm{TC}(\pi)$ equals $\mathrm{cd}(\pi\times\pi)$ for certain toral relatively hyperbolic groups $\pi$.