The Morita classes are nonzero

Abstract

We prove that all Morita classes $\mu_k \in H_{4k}(Aut(F_{2k+2});\mathbb{Q})$ are nonzero using a novel description of the Hopf algebra structure on Steinberg homology. We prove analogous results with twisted coefficients. Our results disprove a case of a finiteness conjecture of Kontsevich.