Homology and cohomology of manifolds

  • Frédéric Pham
Part of the Universitext book series (UTX)


Chains on a manifold (following De Rham). Stokes’ formula, the boundary, chain transformations. Homology, torsion, retractions, homotopy, deformation-retractions, relative homology. Cohomology, cochains, homotopy, relative cohomology, de Rham duality. Families of supports. Poincaré’s isomorphism and duality, intersection index, Leray coboundary. Currents, the support of a current, the boundary and differential of a current, homology of currents, homologies between currents and differential forms, homologies between currents and chains. A useful example: the current defined by a closed oriented submanifold. Intersection indices.


Topological Space Homology Group Intersection Index Homology Class Tubular Neighbourhood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Frédéric Pham
    • 1
  1. 1.Laboratoire J.-A. DieudonnéUniversité de Nice Sophia AntipolisNice cedex 02France

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