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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References
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, N.J., 1952.
J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., 1961. (Dover)
E. Moise, Geometric Topology in Dimensions 2 and 3, Springer-Verlag, New York, 1977.
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© 1991 Springer Science+Business Media, LLC
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Massey, W.S. (1991). Determination of the Homology Groups of Certain Spaces: Applications and Further Properties of Homology Theory. 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_8
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DOI: https://doi.org/10.1007/978-1-4939-9063-4_8
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Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97430-9
Online ISBN: 978-1-4939-9063-4
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