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.
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Bibliography for Chapter III
E. Artin and R. H. Fox, Some wild cells and spheres in three-dimensional space, Ann. Math. 49 (1948), 979–990.
S. Eilenberg and N. E. Steenrod, Foundations of Algebraic Topology, Princeton University Press, Princeton, 1952.
J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading 1961.
E. Moise, Geometric Topology in Dimensions 2 and 3. Springer-Verlag, New York, 1977.
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© 1980 Springer-Verlag New York Inc.
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Massey, W.S. (1980). Determination of the Homology Groups of Certain Spaces : Applications and Further Properties of Homology Theory. In: Singular Homology Theory. Graduate Texts in Mathematics, vol 70. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9231-6_3
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DOI: https://doi.org/10.1007/978-1-4684-9231-6_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9233-0
Online ISBN: 978-1-4684-9231-6
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