### Kontsevich’s theorem and Morita’s cycles

#### Abstract

Morita’s cycles are an infinite sequence of cycles in the unstable homology of . Their construction is motivated by a remarkable theorem of Kontsevich which relates these homology groups with the cohomology of a certain Lie algebra associated to the Lie operad.

I will define operads, giving plenty of examples, and introduce the unstable range of , showing where these Morita cycles fit in. I’ll then state Kontsevich’s theorem and explain how Mortia’s observation leads to cycles in the homology of .