Equivariant Formality of the Little Disks Operad

By a theorem of Kontsevich and Lambrechts-Volić, the little disks operad is formal in every dimension, meaning that its rational homotopy type is faithfully represented by its cohomology. This theorem has had significant consequences in both high and low-dimensional topology (e.g., Vassiliev invariants, diffeomorphisms of the disk) as well as in deformation theory (e.g., quantization deformation of Poisson manifolds). In my talk, I will review these results and explain a recent result on the equivariant formality of the little disks operad.

This is joint work with Pedro Boavida de Brito and Joana Cirici.