The Farrell-Jones Conjecture for Graph Products

TL;DR

This paper proves that the class of groups satisfying the Farrell-Jones conjecture remains closed when forming graph products, expanding the understanding of the conjecture's stability under group operations.

Contribution

It establishes that the Farrell-Jones conjecture is preserved under graph product constructions, a significant extension of known closure properties.

Findings

The class of Farrell-Jones groups is closed under graph products.

Graph product groups satisfy the K- and L-theoretic Farrell-Jones conjecture.

The result broadens the applicability of the conjecture to complex group constructions.

Abstract

We show that the class of groups satisfying the K- and L-theoretic Farrell-Jones conjecture is closed under taking graph products of groups.