The rational homotopy of mapping spaces of E${}_n$ operads

Benoit Fresse, Victor Turchin, Thomas Willwacher

We express the rational homotopy type of the mapping spaces ${\mathrm{Map}}^h({\mathsf{D}}_m,{\mathsf{D}}_n^{\mathbb{Q}})$ of the little discs operads in terms of graph complexes. Using kno…