Coxeter Complexes and Graph-Associahedra

Details Coxeter Complexes and Graph-Associahedra Coxeter Complexes and Graph-Associahedra

2004-07-13

arxiv.org/abs/math/0407229v2

Topology and its Applications, 153 (2006) 2155-2168

Mathematics

Quantum Algebra

18 pages, 9 figures; revised content and references

Scientific paper

Given a graph G, we construct a simple, convex polytope whose face poset is based on the connected subgraphs of G. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The geometric and combinatorial properties of the complex as well as of the polyhedra are given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford compactification of the real moduli space of curves.

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