Abstract
The purpose of this chapter is to develop a systematic procedure for determining the homology groups of a ceetain 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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
N. Bourbaki, General Topology, Part 2, Addison-Wesley, Reading, Mass., 1966.
G. E. Cooke and R. L. Finney, Homology of Cell Complexes, Princeton University Press, Princeton, N.J., 1967.
P. J. Hilton, An Introduction to Homotopy Theory, Cambridge University Press, New York, 1953, Chapter VII.
S. T. Hu, Elements of General Topology, Holden-Day, San Francisco, 1964, Chapter IV.
A. T. Lundell and S. Weingram, The Topology of CW-complexes, Van Nostrand Reinhold Co., New York, 1969.
W. S. Massey, Algebraic Topology: An Introduction, Springer-Verlag, New York, 1977, pp. 215–217.
W. S. Massey, Homology and Cohomology Theory: An Approach Based on Alexander-Spanier Cochains, Marcel Dekker, Inc., Now York, 1978, Chapter 5.
R. Brown, Elements of Modern Topology, McGraw-Hill Co., New York, 1968. Chapter 5.
H. Seifert and W. Threlfall, A Textbook of Topology, Academic Press, New York, 1980.
J. H. C. Whitehead, Combinatorial homotopy I, Bull Am. Math. Soc. 55 (1949), 213–245.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Massey, W.S. (1991). Homology of CW-Complexes. In: A Basic Course in Algebraic Topology. Graduate Texts in Mathematics, vol 127. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9063-4_9
Download citation
DOI: https://doi.org/10.1007/978-1-4939-9063-4_9
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97430-9
Online ISBN: 978-1-4939-9063-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)