We construct a cellular decomposition of the
Axelrod-Singer-Fulton-MacPherson compactification of the configuration
spaces in the plane, that is compatible with the operad composition.
Cells are indexed by trees with bi-coloured edges, and vertices are labelled by
cells of the cacti operad. This answers positively a conjecture stated in
2000 by Kontsevich and Soibelman.
- Topology Seminar