The homology of $\mathrm{Out}(F_8)$ and $\mathrm{Aut}(F_7)$

Maroš Grego, Tomáš Vítek, Thomas Willwacher

We compute the rational homology of $\mathrm{Out}(F_8)$ and $\mathrm{Aut}(F_7)$, and several related groups. We also show that the Eisenstein classes in $H_7(\mathrm{Aut}(F_5))$ an…