The Rational Homology Group of Out(F_n) for n ≤ 6

Abstract

We determine the rational homology group of Out(F_n ) for n ≤ 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 ≤ 6.

Keywords:

• Primary 20J06
• Secondary 20F28, 20F65
• Cohomology of groups
• automorphism groups