`ISRN GeometryVolume 2011 (2011), Article ID 387936, 13 pageshttp://dx.doi.org/10.5402/2011/387936`
Research Article

## An Explicit Description of Coxeter Homology Complexes

1Scuola Normale Superiore di Pisa, 56126 Pisa, Italy
2Dipartimento di Matematica, Università di Pisa, 56127 Pisa, Italy

Received 12 May 2011; Accepted 21 June 2011

Academic Editors: A. Cattaneo and A. Morozov

Copyright © 2011 Filippo Callegaro and Giovanni Gaiffi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. C. de Concini and C. Procesi, “Wonderful models of subspace arrangements,” Selecta Mathematica. New Series, vol. 1, no. 3, pp. 459–494, 1995.
2. E. M. Rains, “The homology of real subspace arrangements,” Journal of Topology, vol. 3, no. 4, pp. 786–818, 2010.
3. P. Etingof, A. Henriques, J. Kamnitzer, and E. M. Rains, “The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points,” Annals of Mathematics. Second Series, vol. 171, no. 2, pp. 731–777, 2010.
4. G. Gaiffi, “Models for real subspace arrangements and stratified manifolds,” International Mathematics Research Notices, no. 12, pp. 627–656, 2003.
5. M. P. Carr and S. L. Devadoss, “Coxeter complexes and graph-associahedra,” Topology and its Applications, vol. 153, no. 12, pp. 2155–2168, 2006.
6. M. Davis, T. Januszkiewicz, and R. Scott, “Fundamental groups of blow-ups,” Advances in Mathematics, vol. 177, no. 1, pp. 115–179, 2003.
7. S. L. Devadoss, “Tessellations of moduli spaces and the mosaic operad,” in Contemporary Mathematics, vol. 239, pp. 91–114, 1999.
8. M. M. Kapranov, “The permutoassociahedron, Mac Lane's coherence theorem and asymptotic zones for the KZ equation,” Journal of Pure and Applied Algebra, vol. 85, no. 2, pp. 119–142, 1993.
9. W. Fulton and R. MacPherson, “A compactification of configuration spaces,” Annals of Mathematics. Second Series, vol. 139, no. 1, pp. 183–225, 1994.
10. M. Kontsevich, “Deformation quantization of Poisson manifolds,” Letters in Mathematical Physics, vol. 66, no. 3, pp. 157–216, 2003.
11. D. P. Sinha, “Manifold-theoretic compactifications of configuration spaces,” Selecta Mathematica. New Series, vol. 10, no. 3, pp. 391–428, 2004.
12. G. Gaiffi, “Real structures of models of arrangements,” International Mathematics Research Notices, no. 64, pp. 3439–3467, 2004.
13. C. de Concini and C. Procesi, “Hyperplane arrangements and holonomy equations,” Selecta Mathematica, vol. 1, no. 3, pp. 495–536, 1995.
14. S. Yuzvinsky, “Cohomology bases for the De Concini-Procesi models of hyperplane arrangements and sums over trees,” Inventiones Mathematicae, vol. 127, no. 2, pp. 319–335, 1997.
15. V. Toledano Laredo, “Quasi-Coxeter algebras, Dynkin diagram cohomology, and quantum Weyl groups,” International Mathematics Research Papers, Article ID rpn009, p. 167, 2008.
16. J. D. Stasheff, “Homotopy associativity of H spaces I.,” Transactions of the American Mathematical Society, vol. 108, pp. 293–312, 1963.
17. A. Postnikov, “Permutohedra, associahedra, and beyond,” International Mathematics Research Notices. IMRN, no. 6, pp. 1026–1106, 2009.
18. A. Postnikov, V. Reiner, and L. Williams, “Faces of generalized permutohedra,” Documenta Mathematica, vol. 13, pp. 207–273, 2008.
19. A. Zelevinsky, “Nested complexes and their polyhedral realizations,” Pure and Applied Mathematics Quarterly, vol. 2, pp. 655–671, 2006.
20. E. M. Feichtner and B. Sturmfels, “Matroid polytopes, nested sets and Bergman fans,” Portugaliae Mathematica. Nova Série, vol. 62, no. 4, pp. 437–468, 2005.
21. A. B. Goncharov and Y. I. Manin, “Multiple $\zeta$-motives and moduli spaces ${\overline{M}}_{0,n}$,” Compositio Mathematica, vol. 140, no. 1, pp. 1–14, 2004.
22. G. Gaiffi and M. Serventi, “Poincarè series for maximal De Concini-Procesi models of root arrangements,” Rendiconti Lincei—Matematica e Applicazioni. In press.
23. A. Henderson and E. Rains, “The cohomology of real de concini-procesi models of coxeter type,” International Mathematics Research Notices, vol. 2008, no. 1, Article ID rnn001, 2008.