What is...?

I’ll describe graph complexes, introduced by Kontsevich in the context of mathematical physics. I’ll survey its connections to geometry and topology, highlighting its relation to the cohomology of moduli spaces of curves. 

For a low-dimensional manifold, one often tries to understand its intrinsic topology and geometry through its submanifolds, in particular of co-dimension 1. To be interesting and to give some information, such a submanifold should interact with the...