## Coxeter complexes and graph-associahedra.(English)Zbl 1099.52001

The authors suggest a construction of a simple convex polytope, called graph-associahedra, which is associated with a given graph $$\Gamma$$ and whose face partial order coincides with the partial order of sets of connected subgraphs of $$\Gamma$$. This construction includes as particular cases the Stasheff associahedron and the Bott-Taubes cyclohedron. In case of simplicial Coxeter groups and respective Coxeter complexes the graph-associahedron represents its fundamental domain. Furthermore, the minimal blow-ups of such Coxeter complexes have tiling by graph-associahedra, which can be viewed as a generalization of the Deligne-Knudsen-Mumford compactification of the real moduli space of rational curves with marked points.

### MSC:

 52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) 05B45 Combinatorial aspects of tessellation and tiling problems 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)

minimal blow-ups
Full Text:

### References:

 [1] S. Armstrong, M. Carr, S. Devadoss, E. Engler, A. Leininger, M. Manapat, Point configurations and Coxeter operads, Preprint, 2004 [2] Bott, R.; Taubes, C., On the self-linking of knots, J. math. phys., 35, 5247-5287, (1994) · Zbl 0863.57004 [3] Bourbaki, N., Lie groups and Lie algebras. chapters 4-6, (2002), Springer Berlin · Zbl 0983.17001 [4] Brown, K.S., Buildings, (1989), Springer New York · Zbl 0715.20017 [5] Davis, M.; Januszkiewicz, T.; Scott, R., Nonpositive curvature of blowups, Selecta math., 4, 491-547, (1998) · Zbl 0924.53033 [6] Davis, M.; Januszkiewicz, T.; Scott, R., Fundamental groups of minimal blow-ups, Adv. math., 177, 115-179, (2003) · Zbl 1080.52512 [7] De Concini, C.; Procesi, C., Wonderful models of subspace arrangements, Selecta math., 1, 459-494, (1995) · Zbl 0842.14038 [8] Devadoss, S., Tessellations of moduli spaces and the mosaic operad, Contemp. math., 239, 91-114, (1999) · Zbl 0968.32009 [9] Devadoss, S., A space of cyclohedra, Discrete comput. geom., 29, 61-75, (2003) · Zbl 1027.52007 [10] Devadoss, S., Combinatorial equivalence of real moduli spaces, Notices amer. math. soc., 51, 620-628, (2004) · Zbl 1093.14509 [11] Fomin, S.; Zelevinsky, A., Y-systems and generalized associahedra, Ann. of math., 158, 977-1018, (2003) · Zbl 1057.52003 [12] Hartshorne, R., Algebraic geometry, (1977), Springer New York · Zbl 0367.14001 [13] Kapranov, M.M., The permutoassociahedron, Maclane’s coherence theorem, and asymptotic zones for the KZ equation, J. pure appl. algebra, 85, 119-142, (1993) · Zbl 0812.18003 [14] Lee, C., The associahedron and triangulations of the n-gon, European J. combin., 10, 551-560, (1989) · Zbl 0682.52004 [15] Stasheff, J.D., Homotopy associativity of H-spaces, Trans. amer. math. soc., 108, 275-292, (1963) · Zbl 0114.39402 [16] Stasheff, J.D., From operads to “physically” inspired theories, Contemp. math., 202, 53-81, (1997), (Appendix B coauthored with S. Shnider) · Zbl 0872.55010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.