About this Journal Submit a Manuscript Table of Contents
ISRN Geometry
Volume 2011 (2011), Article ID 387936, 13 pages
http://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.

Linked References

  1. C. de Concini and C. Procesi, “Wonderful models of subspace arrangements,” Selecta Mathematica. New Series, vol. 1, no. 3, pp. 459–494, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. E. M. Rains, “The homology of real subspace arrangements,” Journal of Topology, vol. 3, no. 4, pp. 786–818, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. G. Gaiffi, “Models for real subspace arrangements and stratified manifolds,” International Mathematics Research Notices, no. 12, pp. 627–656, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Davis, T. Januszkiewicz, and R. Scott, “Fundamental groups of blow-ups,” Advances in Mathematics, vol. 177, no. 1, pp. 115–179, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. S. L. Devadoss, “Tessellations of moduli spaces and the mosaic operad,” in Contemporary Mathematics, vol. 239, pp. 91–114, 1999. View at Zentralblatt MATH
  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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. W. Fulton and R. MacPherson, “A compactification of configuration spaces,” Annals of Mathematics. Second Series, vol. 139, no. 1, pp. 183–225, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Kontsevich, “Deformation quantization of Poisson manifolds,” Letters in Mathematical Physics, vol. 66, no. 3, pp. 157–216, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. P. Sinha, “Manifold-theoretic compactifications of configuration spaces,” Selecta Mathematica. New Series, vol. 10, no. 3, pp. 391–428, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. G. Gaiffi, “Real structures of models of arrangements,” International Mathematics Research Notices, no. 64, pp. 3439–3467, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. C. de Concini and C. Procesi, “Hyperplane arrangements and holonomy equations,” Selecta Mathematica, vol. 1, no. 3, pp. 495–536, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. V. Toledano Laredo, “Quasi-Coxeter algebras, Dynkin diagram cohomology, and quantum Weyl groups,” International Mathematics Research Papers, Article ID rpn009, p. 167, 2008. View at Zentralblatt MATH
  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. View at Zentralblatt MATH
  18. A. Postnikov, V. Reiner, and L. Williams, “Faces of generalized permutohedra,” Documenta Mathematica, vol. 13, pp. 207–273, 2008. View at Zentralblatt MATH
  19. A. Zelevinsky, “Nested complexes and their polyhedral realizations,” Pure and Applied Mathematics Quarterly, vol. 2, pp. 655–671, 2006. View at Zentralblatt MATH
  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. View at Zentralblatt MATH
  21. A. B. Goncharov and Y. I. Manin, “Multiple ζ-motives and moduli spaces M¯0,n,” Compositio Mathematica, vol. 140, no. 1, pp. 1–14, 2004. View at Publisher · View at Google Scholar
  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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH