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Particle configurations and Coxeter operads

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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