Homology and cohomology of manifolds
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.
KeywordsTopological Space Homology Group Intersection Index Homology Class Tubular Neighbourhood
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