Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Vasily Dolgushev
Affiliation:

Temple University
Date:

Sat, 2016-03-19 10:00 - 11:00 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 $\mathrm{Out}(F_r)$ of the free group $F_r$ on $r$ generators, the absolute Galois group $\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ of rationals, finite type invariants of tangles, and the homotopy groups of embedding spaces.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/6477