The Rational Homology Group of $\mathrm{Out}(F_n)$ for $n\leq 6$

Abstract

We determine the rational homology group of $\mathrm{Out}(F_n)$ for $n\leq 6$. Combining this result with results of Conant and Vogtmann proves that the first two Morita classes are nontrivial. We conclude that these classes generate the nontrivial part of the rational homology in the range $n\leq 6$.