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Homology of CW-complexes

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

Abstract

The purpose of this chapter is to develop a systematic procedure for determining the homology groups of a certain class of topological spaces. The class of topological spaces chosen consists of the CW-complexes of J. H. C. Whitehead. The procedure developed is a natural generalization and extension of the method used in the preceding chapter to determine the homology groups of graphs and compact 2-manifolds.

Keywords

Exact Sequence Simplicial Complex Homology Group Homology Class Free Abelian Group 
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 IV

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    N. Bourbaki, Topologie Générale, Hermann et Cie., Paris 1947, Chapters VI and VIII.MATHGoogle Scholar
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    G. E. Cooke and R. L. Finney, Homology of Cell Complexes, Princeton University Press, Princeton, 1967.MATHGoogle Scholar
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    S. T. Hu, Elements of General Topology, Holden-Day, San Francisco, 1964,MATHGoogle Scholar
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    A. T. Lundell and S. Weingram, The Topology of CW-complexes, Van Nostrand Reinhold Co., New York, 1969.MATHCrossRefGoogle Scholar
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    W. S. Massey, Algebraic Topology: An Introduction, Springer-Verlag, New York, 1977, pp. 215–217.Google Scholar
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    W. S Massey, Homology and Cohomology Theory: An Approach Based onAlexander-Spanier Cochains, Marcel Dekker, Inc., New York, 1978, Chapter 5.Google Scholar
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    H. Seifert and W. Threlfall, Lehrbuch der Topologie, Chelsea Publishing Co., New York, 1947.Google Scholar
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    J. H. C. Whitehead, Combinatorial homotopy I, Bull Amer. Math. Soc. 55 (1949), 213–245.MathSciNetMATHCrossRefGoogle 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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