On the K-theory of certain extensions of free groups

TL;DR

This paper demonstrates that the K-theoretic Farrell-Jones Conjecture with coefficients (K-FJCw) holds for specific subgroups of automorphism groups of free groups, built from holomorphs of free groups of rank 2.

Contribution

It establishes the validity of the K-FJCw for new classes of subgroups of automorphism groups of free groups derived from Hol($F_2$).

Findings

K-FJCw holds for certain subgroups of Aut($F_n$).

The subgroups are constructed from Hol($F_2$).

Provides new cases where the conjecture is verified.

Abstract

We show that the K-FJCw holds for certain subgroups of Aut($F_n$) constructed from Hol($F_2$).