A cell decomposition of the Fulton MacPherson operad. Issue 2 (30th April 2022) - Salvatore, Paolo
Abstract: We construct a small regular cellular decomposition of the Fulton MacPherson operad F M 2 $FM_2$ that is compatible with the operad composition. The cells are indexed by trees with edges of two colors and vertices labeled by cells of the cacti operad. We compute the generating functions counting the cells that are algebraic.