Homology Groups

  • Gregory L. Naber
Part of the Texts in Applied Mathematics book series (TAM, volume 25)


The homotopy groups πn(X, x0) of a space are relatively easy to define, clearly topological invariants and, indeed, invariants of homotopy type, but are also extraordinarily difficult to compute even for quite simple spaces. Now we intend to provide a brief introduction to another set of invariants for which this situation is reversed. The singular homology groups require some work to define and their homotopy invariance is not so obvious, but once some basic tools are developed their computation is comparatively straightforward.


Chain Complex Homology Group Short Exact Sequence Homology Class Free Abelian Group 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Gregory L. Naber
    • 1
  1. 1.Department of MathematicsDrexel UniversityPhiladelphiaUSA

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