Overview of Cubical Homology

  • Akihiko Hirata
  • Kaname Matsue
  • Mingwei Chen
Part of the SpringerBriefs in the Mathematics of Materials book series (BRIEFSMAMA, volume 2)


In this chapter, we briefly review the concept of homology, which lies at the center of our analysis concerning the structure of metallic glasses. Homology measures topological complexity, such as the number of connected components and holes, of given objects from the algebraic viewpoint.


Metallic Glass Simplicial Complex Homology Group Betti Number Geometric Object 
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  1. 1.
    T. Kaczynski, K. Mischaikow, and M. Mrozek. Computational Homology, Springer Applied Mathematical Sciences vol. 157, 2004.Google Scholar
  2. 2.
    E. Frenkel. Love and Math: The Heart of Hidden Reality, Basic Books, 2013.Google Scholar
  3. 3.
    CHomP: Computational Homology Project.
  4. 4.
    H. Edelsbrunner and J. Harer. Computational Topology: An Introduction. American Mathematical Society, 2010.Google Scholar
  5. 5.
    RedHom: a part of the CAPD project.

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Advanced Institute for Materials ResearchTohoku UniversitySendaiJapan
  2. 2.The Institute of Statistical MathematicsTachikawaJapan

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