The topological complexity of the free product

TL;DR

This paper establishes a formula for the topological complexity of free products of groups, linking it to the maximum of individual complexities and the cohomological dimension of their product.

Contribution

It provides a new explicit formula for the topological complexity of free products of groups with cohomological dimension greater than two.

Findings

Topological complexity of free products equals the maximum of individual complexities and the cohomological dimension of their product.

The formula applies specifically to groups with cohomological dimension greater than two.

Abstract

We prove the formula $TC(G\ast H)=\max\{TC(G), TC(H), cd(G\times H)\}$ for the topological complexity of the free product of discrete groups with cohomological dimension >2.