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 


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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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