On the homology of automorphism groups of free groups.

Following the work of Conant and Vogtmann on determining the homology of the group of outer automorphisms of a free group, a new nontrivial class in the rational homology of Outer space is established for the free group of rank eight. The methods started in [8] are heavily exploited and used to create a new graph complex called the space of good chord diagrams. This complex carries with it significant computational advantages in determining possible nontrivial homology classes.
Next, we create a basepointed version of the Lie operad and explore some of it proper- ties. In particular, we prove a Kontsevich-type theorem that relates the Lie homology of a particular space to the cohomology of the group of automorphisms of the free group.