Particle Configurations and Coxeter Operads

Details Particle Configurations and Coxeter Operads Particle Configurations and Coxeter Operads

2005-02-08

arxiv.org/abs/math/0502159v3

Homotopy and Related Structures, Volume 4 (2009) 83-109.

Mathematics

Geometric Topology

25 pages, 18 figures; revision of Coxeter operads

Scientific paper

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.

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