Homology Theory and Abelianization

  • John Stillwell
Part of the Graduate Texts in Mathematics book series (GTM, volume 72)


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.


Abelian Group Homology Group Betti Number Finite Order Structure Theorem 
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Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia

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