Homology of holomorphs of free groups

الأصل · EN

The holomorph of a free group Fₙ is the semidirect product Fₙ Aut(Fₙ). 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(Fₙ) acts by first projecting to Glₙ() and then including in Glₙ()) homology H*(Aut(Fₙ); ⁿ) follow in corresponding dimensions.