Homology of holomorphs of free groups

Abstract

The holomorph of a free group $F_n$ is the semidirect product $F_n⋊Aut(F_n)$. Using the methods of Hatcher and Vogtmann, we derive stability results and calculate the mod-$p$ homology of these holomorphs for odd primes $p$ in dimensions 1 and 2, and their rational homology in dimensions 1 through 5. Calculations of the twisted (where $Aut(F_n)$ acts by first projecting to $G{l}_n(\mathbb{Z})$ and then including in $Gl_n(\Q)$) homology $H_*(Aut(F_n); \Q^n)$ follow in corresponding dimensions.

Revised using helpful comments of referee. Accepted by J. Algebra. J. Algebra has agreed to host the Maple program files (currently on my web page) on their site