A Homological–Based Description of Subdivided nD Objects

  • Helena Molina-Abril
  • Pedro Real
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6854)


We present here a topo–geometrical description of a subdivided nD object called homological spanning forest representation. This representation is a convenient tool in order to completely control not only geometrical, but also advanced topological information of a given object. By codifying the underlying algebraic topological machinery in terms of coordinate–based graphs, we progress in the task to “combinatorialize” homological information at two levels: local and global. Therefore, our method presents several advantages with respect to the existing Algebraic topological models, and techniques based in Discrete Morse Theory. A construction algorithm has been implemented, and some examples are shown.


Chain Complex Cell Complex Critical Cell Barycentric Subdivision Harmonic Complex 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Helena Molina-Abril
    • 1
    • 2
  • Pedro Real
    • 1
  1. 1.Computational Topology and Applied Mathematics GroupUniversity of SevilleSpain
  2. 2.Pattern Recognition and Image Processing GroupVienna University of TechnologySpain

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