An improvement of the Farrell-Jones conjecture for localising invariants

TL;DR

This paper proves that the Farrell-Jones conjecture for localising invariants holds without requiring the lax monoidal assumption, simplifying the conditions needed for its validity.

Contribution

It removes the lax monoidal assumption from the Farrell-Jones conjecture for localising invariants using noncommutative motives, advancing the theoretical understanding.

Findings

Lax monoidal assumption is unnecessary for the conjecture.

The proof utilizes noncommutative motives.

The result broadens the applicability of the conjecture.

Abstract

The Farrell-Jones conjecture for lax monoidal finitary localising invariants was recently proved by Bunke-Kasprowski-Winges. In this short note, making use of the theory of noncommutative motives, we prove that the lax monoidal assumption is not necessary.