The A-theoretic Farrell-Jones Conjecture for virtually solvable groups

TL;DR

This paper proves the A-theoretic Farrell-Jones Conjecture for virtually solvable groups, extending its validity to S-arithmetic groups and lattices in almost connected Lie groups, thereby advancing understanding in algebraic K-theory.

Contribution

It establishes the conjecture for a broad class of groups, including virtually solvable, S-arithmetic, and certain Lie group lattices, which was previously unknown.

Findings

Proves the A-theoretic Farrell-Jones Conjecture for virtually solvable groups.

Extends the conjecture's validity to S-arithmetic groups.

Confirms the conjecture for lattices in almost connected Lie groups.

Abstract

We prove the A-theoretic Farrell-Jones Conjecture for virtually solvable groups. As a corollary, we obtain that the conjecture holds for S-arithmetic groups and lattices in almost connected Lie groups.