Homology of CW-complexes

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


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.


Exact Sequence Simplicial Complex Homology Group Homology Class Free Abelian Group 
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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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    P. J. Hilton, An Introduction Homotopy Theory, Cambridge University Press, New York, 1953, Chapter VII.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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    I. R. Porteous, Topological Geometry, Van Nostrand Reinhold Co., New York, 1969.MATHGoogle 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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