Homology of holomorphs of free groups

Details Homology of holomorphs of free groups Homology of holomorphs of free groups

2001-12-18

arxiv.org/abs/math/0112187v2

Mathematics

Group Theory

Revised using helpful comments of referee. Accepted by J. Algebra. J. Algebra has agreed to host the Maple program files (curr

Scientific paper

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.

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