• Anatolij T. Fomenko
  • Tosiyasu L. Kinii


In this chapter we associate to certain topological spaces a sequence of abelian groups, called homology groups, H r (K), for r = 0, 1, .... These groups give us information on the topological structure of K. For instance, H 0(K) measures the number of connected components of the space; the higher homology groups H r (K), for r > 0, intuitively speaking, measure the number of “r-dimensional holes” in K. A one-dimensional hole is a hole in the ordinary sense, a two-dimensional hole is an enclosed space, and so on.


Abelian Group Topological Space Boundary Operator Simplicial Complex Homology Group 
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Copyright information

© Springer Japan 1997

Authors and Affiliations

  • Anatolij T. Fomenko
    • 1
  • Tosiyasu L. Kinii
    • 2
    • 3
  1. 1.Department of Differential Geometry and Application, Faculty of Mathematics and MechanicsMoscow State UniversityMoscowRussia
  2. 2.Laboratory of Digital Art and TechnologyTokyo, 113Japan
  3. 3.Senior Partner of MONOLITH Co. Ltd.Tokyo, 106Japan

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