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

#### Abstract

Morita’s cycles are an infinite sequence of cycles in the unstable homology of $\mbox{Out}(F_n)$. Their construction is motivated by a remarkable theorem of Kontsevich which relates these homology groups with the cohomology of a certain Lie algebra $\mathfrak{h}_\infty$ associated to the Lie operad.

I will define operads, giving plenty of examples, and introduce the unstable range of $H_\ast(\mbox{Out}(F_n))$, 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 $\mbox{Out}(F_n)$.

#### Slides

Slides as a (large) PDF
Slides as a keynote

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