The holomorph of a free group $F_n$ is the semidirect product $F_n \rtimes
Aut(F_n)$. 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
$Gl_n(\Z)$ and then including in $Gl_n(\Q)$) homology $H_*(Aut(F_n); \Q^n)$
follow in corresponding dimensions.Comment: 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 sit

Jensen, Craig A.

English

arXiv

Let Fn be the free group on n letters and let Aut(Fn), Out(Fn) denote the automorphism group and the outer automorphism group of Fn. In this paper the purpose is to obtain some new results on stability and to calculate the mod-p homology of the holomorph of Fn for odd primes in dimensions 1 and 2, and the rational homology in dimensions from 1 through 5

Jensen, Craig A

ScholarWorks @ The University of New Orleans

Homology of Holomorphs of Free Groups

AbstractThe holomorph of a free group Fn is the semidirect product Fn⋊Aut(Fn). Using the methods of Hatcher and Vogtmann in [J. London Math. Soc. (2) 58 (1998) 633–635 and Math. Res. Lett. 5 (1998) 759–780], 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(Fn) acts by first projecting to Gln(Z) and then including in Gln(Q)) homology H∗(Aut(Fn);Qn) follow in corresponding dimensions

Homology of holomorphs of free groups

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