Advertisement

Homology of Simploidal Set

  • Samuel Peltier
  • Laurent Fuchs
  • Pascal Lienhardt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)

Abstract

In this article the homology of simploidal sets is studied. Simploidal sets generalize both simplicial complexes and cubical complexes, more precisely cells of simplicial sets are cartesian products of simplices. We define one homology for simploidal sets and we prove that this homology is equivalent to the homology usually defined on simplicial complexes.

Keywords

Boundary Operator Simplicial Complex Homology Group Simplicial Cycle Constructive Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Dahmen, W., Micchelli, C.A.: On the linear independence of multivariate b-splines I. Triangulation of simploids. SIAM J. Numer. Anal. 19 (1982)Google Scholar
  2. 2.
    Moore, D.: V.10 Understanding simploids. In: Graphic Gems III, pp. 250–255. Academic Press, London (1992)Google Scholar
  3. 3.
    Allili, M., Corriveau, D., Ziou, D.: Morse homology desriptor for shape characterization. In: Proc. ICPR (2004)Google Scholar
  4. 4.
    Munkres, J.R.: Elements of algebraic topology. Perseus Books (1984)Google Scholar
  5. 5.
    Lang, V., Lienhardt, P.: Geometric modeling with simplicial sets. In: Proc. of Pacific Graphics 1995, Seoul, Korea (1995)Google Scholar
  6. 6.
    Kaczynski, T., Mischaikow, K., Mrozek, M.: Computational Homology. Springer, Heidelberg (2004)MATHGoogle Scholar
  7. 7.
    Peltier, S., Alayrangues, S., Fuchs, L., Lachaud, J.-O.: Computation of homology groups and generators. In: Andrès, É., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 195–205. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Fuchs, L., Lienhardt, P.: Topological structures and free-form spaces. In: Journes franco-espagnoles de gomtrie algorithmique, pp. 35–46 (1997)Google Scholar
  9. 9.
    Lienhardt, P., Skapin, X., Bergey, A.: Cartesian product of simplicial and cellular structures. Int. Journal of Computational Geometry and Applications 14(3), 115–159 (2004)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Peltier, S.: Calcul de groupes d’homologie sur des structures simpliciales, simploidales et cellulaires. PhD thesis, Université de Poitiers (to appear, 2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Samuel Peltier
    • 1
  • Laurent Fuchs
    • 1
  • Pascal Lienhardt
    • 1
  1. 1.SIC, Université de PoitiersFuturoscope ChasseneuilFrance

Personalised recommendations