From acyclic groups to the bass conjecture for amenable groups

TL;DR

This paper demonstrates that the Bost Conjecture implies the Bass Conjecture for countable discrete groups, establishing that all amenable groups satisfy the Bass Conjecture.

Contribution

It proves that the Bost Conjecture implies the Bass Conjecture, confirming the conjecture for all amenable groups.

Findings

Bost Conjecture implies Bass Conjecture for countable groups

All amenable groups satisfy the Bass Conjecture

Establishes a link between two major conjectures in group theory

Abstract

We prove that the Bost Conjecture on the $\ell^1$-assembly map for countable discrete groups implies the Bass Conjecture. It follows that all amenable groups satisfy the Bass Conjecture.