Differential forms in algebraic topology. Transl. from the English by I. V. Savel’ev and G. S. Shmelev. Transl. ed. by A. A. Kirillov. (Дифференциальные формы в алгебраической топологии.) (Russian) Zbl 0675.55002

Bott, Raoul; Tu, Loring W.

Moskva: Nauka. 336 p. R. 3.20 (1989).

See the review of the English original (New York, 1982) in Zbl 0496.55001.

MSC:

55-02	Research exposition (monographs, survey articles) pertaining to algebraic topology
58-02	Research exposition (monographs, survey articles) pertaining to global analysis
58A12	de Rham theory in global analysis
57R20	Characteristic classes and numbers in differential topology
55N05	Čech types
55N10	Singular homology and cohomology theory
55R05	Fiber spaces in algebraic topology
55R10	Fiber bundles in algebraic topology
55R15	Classification of fiber spaces or bundles in algebraic topology
55R20	Spectral sequences and homology of fiber spaces in algebraic topology
55R25	Sphere bundles and vector bundles in algebraic topology
55R40	Homology of classifying spaces and characteristic classes in algebraic topology
55T05	General theory of spectral sequences in algebraic topology
55T10	Serre spectral sequences
55P62	Rational homotopy theory
55P20	Eilenberg-Mac Lane spaces
55Q05	Homotopy groups, general; sets of homotopy classes
55Q25	Hopf invariants
55Q40	Homotopy groups of spheres
57R19	Algebraic topology on manifolds and differential topology
57R25	Vector fields, frame fields in differential topology
58A05	Differentiable manifolds, foundations
58A10	Differential forms in global analysis

Keywords:

de Rham theory; singular (co)homology; Eilenberg-Steenrod axioms; Čech-de Rham complex; spectral sequences; characteristic classes; de Rham cohomology; integration of differential forms; Stoke’s theorem; Poincare lemmas; Poincare duality; Kuenneth formula; Leray-Hirsch theorem; Thom isomorphism; vector bundles; vertical cohomology; integration along the fiber; Thom class; Euler class; twisted de Rham complex; Cech cohomology; Hopf index theorem; cohomology of complex projective spaces; Gysin sequence; universal coefficient theorems; cohomology of loop spaces; Hurewicz isomorphism; Morse theory; Hopf fibration; Hopf invariant; Eilenberg-MacLane spaces; transgressive elements; Postnikov approximation; homotopy groups of a sphere; rational homotopy theory

Citations:

Zbl 0442.55001; Zbl 0047.16702; Zbl 0496.55001