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)

Abstract

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.

Keywords

Chain Complex Cell Complex Critical Cell Barycentric Subdivision Harmonic Complex 
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.

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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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