Éléments d’analyse. Tome IX. Chapitre XXIV. (French) Zbl 0485.58001

Dieudonné, Jean

Cahiers Scientifiques, Fasc. XLII. Publie avec le concours du C. N. R. S. Paris: Gauthier-Villars. XVIII, 380 p. FF 320.00 (1982).

MSC:

58-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis
55-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology
58A12	de Rham theory in global analysis
55Rxx	Fiber spaces and bundles in algebraic topology
58A14	Hodge theory in global analysis
58A10	Differential forms in global analysis
20G10	Cohomology theory for linear algebraic groups
17B56	Cohomology of Lie (super)algebras
57Q05	General topology of complexes
55N10	Singular homology and cohomology theory
53C05	Connections (general theory)
14F40	de Rham cohomology and algebraic geometry
14H05	Algebraic functions and function fields in algebraic geometry
58J10	Differential complexes
58J20	Index theory and related fixed-point theorems on manifolds

Keywords:

homology and the cohomology of differentiable manifolds and fibre spaces; cohomology with compact supports; Mayer-Vietoris sequences; Kuenneth theorem; Poincare duality; degree theory; intersection numbers; Stokes formula; algebraic equations; intersections of algebraic curves; homology of cellular currents; simplicial spaces; simplicial currents; Gysin exact sequence; Euler class; cohomology of Grassmann manifolds; characteristic classes; Chern classes; Pontrjagin classes; Stiefel-Whitney classes; elliptic complexes of pseudo-differential operators; Atiyah-Bott- Lefschetz formula; Hopf formula for vector fields; formulas of Bott for characteristic classes; cohomology of a Lie group

Citations:

Zbl 0189.055; Zbl 0208.318; Zbl 0217.001; Zbl 0326.22001; Zbl 0303.43001; Zbl 0402.58011; Zbl 0393.35001