Farrell-Jones Conjecture for fundamental groups of graphs of virtually cyclic groups

TL;DR

This paper proves the Farrell-Jones Conjecture for fundamental groups of graphs of virtually cyclic groups, advancing understanding in algebraic K- and L-theory related to these groups.

Contribution

It establishes the Farrell-Jones Conjecture for a new class of groups, namely fundamental groups of graphs of virtually cyclic groups.

Findings

Proof of the Farrell-Jones Conjecture for these groups

Extension of the conjecture to groups with specific graph structures

Implications for algebraic K- and L-theory

Abstract

In this note, we prove the K- and L-theoretic Farrell-Jones Conjecture with coefficients in an additive category for fundamental groups of graphs of virtually cyclic groups.