With hindsight, one can say that homology theory began with the Descartes-Euler polyhedron formula (1.3.8). It took a further step with Riemann’s definition of the connectivity of a surface, and the generalization to higher-dimensional connectivities by Betti 1871. All these results have to do with the computation of numerical invariants of a manifold by means of decomposition into “cells”; the computations involve only the numbers of cells and the incidence relations between them, and it is shown that certain numbers are independent of the particular cellular subdivision chosen.
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Author information Authors and AffiliationsDepartment of Mathematics, Monash University, Clayton, Victoria, 3168, Australia
John Stillwell
© 1993 Springer-Verlag New York Inc.
About this chapter Cite this chapterStillwell, J. (1993). Homology Theory and Abelianization. In: Classical Topology and Combinatorial Group Theory. Graduate Texts in Mathematics, vol 72. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4372-4_6
Download citationDOI: https://doi.org/10.1007/978-1-4612-4372-4_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97970-0
Online ISBN: 978-1-4612-4372-4
eBook Packages: Springer Book Archive
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