Algebraic topology: a student's guide / J. F. Adams

Auteur: Adams, John Frank (1930-1989) - AuteurType de document: MonographieCollection: London Mathematical Society lecture note series ; 4Langue: anglaisPays: Grande BretagneÉditeur: Cambridge : Cambridge University Press, 1972Description: 1 vol. (VI-300 p.) ; 23 cm ISBN: 9780521080767 ; br. Résumé: This volume contains two sections. The first section, pp. 1–31, contains a description of the topics that the author feels ought to be learned by any young mathematician interested in algebraic topology. This part is keyed to a variety (40) of textbooks, with the author's preferences marked by asterisks. After a section describing what he hopes would be covered in a first course in algebraic topology, the author gives his recommendations for the following topics: categories and functors (as used in algebraic topologymostly a list of references), semi-simplicial complexes, ordinary homology and cohomology, spectral sequences, study of H∗(BG), Eilenberg-Mac Lane spaces and the Steenrod algebra, Serre's theory of classes of algebraic groups, obstruction theory, homotopy theory (suspension theory, explicit constructions and the method of Killing homotopy groups) fibre bundles and topology of groups (and characteristic classes and H-spaces), generalized cohomology theories, some survey of the current "state-of-the-art''. The second section contains excerpts from a number of famous papers (sometimes the whole paper) in algebraic topology plus two brief surveys (of generalized cohomology theories and complex cobordism) written by the author. The aim behind this seems to be both to accustom the student to reading research papers and also to acquaint him (or her) with well-written papers. (MathSciNet).Bibliographie: Bibliogr.. Sujets MSC: 55T05 Algebraic topology -- Spectral sequences -- General
55S35 Algebraic topology -- Operations and obstructions -- Obstruction theory
55S10 Algebraic topology -- Operations and obstructions -- Steenrod algebra
55Q05 Algebraic topology -- Homotopy groups -- Homotopy groups, general; sets of homotopy classes
55Nxx Algebraic topology -- Homology and cohomology theories
55Pxx Algebraic topology -- Homotopy theory
En-ligne: Zentralblatt | MathSciNet
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Bibliogr.

This volume contains two sections. The first section, pp. 1–31, contains a description of the topics that the author feels ought to be learned by any young mathematician interested in algebraic topology. This part is keyed to a variety (40) of textbooks, with the author's preferences marked by asterisks. After a section describing what he hopes would be covered in a first course in algebraic topology, the author gives his recommendations for the following topics: categories and functors (as used in algebraic topologymostly a list of references), semi-simplicial complexes, ordinary homology and cohomology, spectral sequences, study of H∗(BG), Eilenberg-Mac Lane spaces and the Steenrod algebra, Serre's theory of classes of algebraic groups, obstruction theory, homotopy theory (suspension theory, explicit constructions and the method of Killing homotopy groups) fibre bundles and topology of groups (and characteristic classes and H-spaces), generalized cohomology theories, some survey of the current "state-of-the-art''. The second section contains excerpts from a number of famous papers (sometimes the whole paper) in algebraic topology plus two brief surveys (of generalized cohomology theories and complex cobordism) written by the author. The aim behind this seems to be both to accustom the student to reading research papers and also to acquaint him (or her) with well-written papers. (MathSciNet)

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