Algebraic topology via differential geometry / M. Karoubi, C. Leruste

Auteur: Karoubi, Max (1938-) - AuteurCo-auteur: Leruste, Christian - AuteurType de document: MonographieCollection: London Mathematical Society lecture note series ; 99Langue: anglaisPays: Grande BretagneÉditeur: Cambridge : Cambridge University Press, 1989Description: 1 vol. (363 p.) ; 23 cm ISBN: 9780521317146 ; br. Résumé: In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry. (source : CUP).Bibliographie: Bibliogr. p.360. Index. Sujets MSC: 55N35 Algebraic topology -- Homology and cohomology theories -- Other homology theories
57R19 Manifolds and cell complexes -- Differential topology -- Algebraic topology on manifolds
58A12 Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- de Rham theory
55M05 Algebraic topology -- Classical topics -- Duality
55M20 Algebraic topology -- Classical topics -- Fixed points and coincidences
55U25 Algebraic topology -- Applied homological algebra and category theory -- Homology of a product, Künneth formula
En-ligne: Zentralblatt | MathSciNet | CUP
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Bibliogr. p.360. Index

In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry. (source : CUP)

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