On unstable twisted rational cohomology groups of the automorphism groups of free groups (New developments of transformation groups)

Abstract

In this article, we consider unstable twisted rational cohomology groups of the automorphism groups of free groups. First, we exposit that there are nontrivial unstable twisted 2-cocycles which are constructed by Kawazumi's cocycles. Second, we exposit a calculation of the second and the third cohomology groups of the automorphism group of free group of rank three with coefficients in the exterior products of the abelianization of the free group.