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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)

Abstract

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.

Keywords

Fundamental Group Regular Graph Homology Group Homology Class Algebraic Topology 
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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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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