Determination of the Homology Groups of Certain Spaces : Applications and Further Properties of Homology Theory

  • William S. Massey
Part of the Graduate Texts in Mathematics book series (GTM, volume 70)


In this chapter, we will actually determine the homology groups of various spaces : the n-dimensional sphere, finite graphs, and compact 2-dimensional manifolds. We also use homology theory to prove some classical theorems of topology, most of which are due to L. E. J. Brouwer. In addition, we prove some more basic properties of homology groups.


Fundamental Group Regular Graph Homology Group Homology Class Algebraic Topology 
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Bibliography for Chapter III

  1. [1]
    E. Artin and R. H. Fox, Some wild cells and spheres in three-dimensional space, Ann. Math. 49 (1948), 979–990.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    S. Eilenberg and N. E. Steenrod, Foundations of Algebraic Topology, Princeton University Press, Princeton, 1952.MATHGoogle Scholar
  3. [3]
    J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading 1961.MATHGoogle Scholar
  4. [4]
    E. Moise, Geometric Topology in Dimensions 2 and 3. Springer-Verlag, New York, 1977.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • William S. Massey
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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