The quantitative coarse Baum-Connes conjecture for free products

TL;DR

This paper proves the quantitative coarse Baum-Connes conjecture for free products of finitely generated groups, assuming the conjecture holds for each factor group.

Contribution

It extends the validity of the conjecture from individual groups to their free product, under specific assumptions.

Findings

Proves the conjecture for free products of groups where it holds for each factor.

Provides a method to transfer the conjecture's validity from groups to their free product.

Abstract

Let $G$ and $H$ be finitely generated groups. In this paper, we prove the quantitative coarse Baum--Connes conjecture for the free product $G* H$ under the assumption that the conjecture holds for both $G$ and $H$.