# Hebrew University topology and geometry seminar

June 15, 2016

1100-1235

Ross building, Seminar Room 70A

## Vasily Dolgushev

*Temple University
*

##
The Intricate Maze of Graph Complexes

**Abstract:**
In the paper "Formal noncommutative symplectic geometry'', Maxim Kontsevich introduced
three versions of cochain complexes $\mathcal{GC}_{\text{Com}}$, $\mathcal{GC}_{\text{Lie}}$ and $\mathcal{GC}_{\text{As}}$
"assembled from'' graphs with some additional structures. The graph complex $\mathcal{GC}_{\text{Com}}$
(resp. $\mathcal{GC}_{\text{Lie}}$, $\mathcal{GC}_{\text{As}}$) is related to the operad $\text{Com}$ (resp. $\text{Lie}$, $\text{As}$)
governing commutative (resp. Lie, associative) algebras. Although the graphs complexes
$\mathcal{GC}_{\text{Com}}$, $\mathcal{GC}_{\text{Lie}}$ and $\mathcal{GC}_{\text{As}}$ (and their generalizations) are easy to define,
it is hard to get very much information about their cohomology spaces. In my talk, I
will describe the links between these graph complexes (and their modifications) to the
cohomology of the moduli spaces of curves, the group of outer automorphisms $\text{Out}(F_r)$ of the
free group $F_r$ on $r$ generators, the absolute Galois group $\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$
of rationals, finite type invariants of tangles, and the homotopy groups of embedding
spaces.