Particle configurations and Coxeter operads

Suzanne M. Armstrong, Michael Carr, Satyan L. Devadoss, Eric Engler, Ananda Leininger, Michael Manapat

There exist natural generalizations of the real moduli space of Riemann spheres based on manipulations of Coxeter complexes. These novel spaces inherit a tiling by the graph-associahedra convex polytopes. We obtain explicit configuration space models for the classical infinite families of finite and affine Weyl groups using particles on lines and circles. A Fulton-MacPherson compactification of these spaces is described and this is used to define the Coxeter operad. A complete classification of the building sets of these complexes is also given, along with a computation of their Euler characteristics.

Journal of Homotopy and Related Structures, Vol. 4(2009), No. 1, pp. 83-109