Topology Seminar: Pascal Lambrechts (UCL Louvain)

The little $n$-dimensional disks operad is a fundamental object in algebraic topology and in some other fields. In particular it is a structure which encodes the natural multiplicative structure on iterated loop spaces, more generally multiplicative structures which are commutative "up to homotopy", and it is also central in Goodwillie-Weiss manifold calculus theory that describes spaces of smooth embeddings of some manifold into another.

In this talk I will explain various statement about the formality of the little operad, that is the fact that its rational homotopy type is completely encoded in its homology, and the key ideas of the proof. This was initially sketched by Kontsevich and we make his result precise and generalize it.

Joint work with Ismar Volic.