## The rational homology group of $$\text{Out}(F_n)$$ for $$n\leq 6$$.(English)Zbl 1191.20057

Summary: We determine the rational homology group of $$\text{Out}(F_n)$$ 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 $$n\leq 6$$.

### MSC:

 20J06 Cohomology of groups 20E05 Free nonabelian groups 20F28 Automorphism groups of groups 20F65 Geometric group theory
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