A User's Guide to Algebraic Topology

Bild: 9780792342939 | A User's Guide to Algebraic Topology | P. E. Parker (u. a.) | Buch

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Beschreibung

We have tried to design this book for both instructional and reference use, during and after a first course in algebraic topology aimed at users rather than developers; indeed, the book arose from such courses taught by the authors. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. A certain amount of redundancy is built in for the reader's convenience: we hope to minimize :fiipping back and forth, and we have provided some appendices for reference. The first three are concerned with background material in algebra, general topology, manifolds, geometry and bundles. Another gives tables of homo topy groups that should prove useful in computations, and the last outlines the use of a computer algebra package for exterior calculus. Our approach has been that whenever a construction from a proof is needed, we have explicitly noted and referenced this. In general, wehavenot given a proof unless it yields something useful for computations. As always, the only way to un derstand mathematics is to do it and use it. To encourage this, Ex denotes either an example or an exercise. The choice is usually up to you the reader, depending on the amount of work you wish to do; however, some are explicitly stated as ( unanswered) questions. In such cases, our implicit claim is that you will greatly benefit from at least thinking about how to answer them.

Inhaltsverzeichnis

Preface. Introduction and Overview. 1. Basics of Extension and Lifting Problems. 2. Up to Homotopy is Good Enough. 3. Homotopy Group Theory. 4. Homology and Cohomology Theories. 5. Examples in Homology and Cohomology. 6. Sheaf and Spectral Theories. 7. Bundle Theory. 8. Obstruction Theory. 9. Applications. A: Algebra. B: Topology. C: Manifolds and Bundles. D: Tables of Homotopy Groups. E: Computational Algebraic Topology. Bibliography. Index.

Details

Erscheinungsjahr:	1997
Fachbereich:	Geometrie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 410 S. 29 s/w Illustr.
ISBN-13:	9780792342939
ISBN-10:	0792342933
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Parker, P. E. Dodson, C. T.
Hersteller:	Springer US Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 23 mm
Von/Mit:	P. E. Parker (u. a.)
Erscheinungsdatum:	31.01.1997
Gewicht:	0,639 kg

Artikel-ID: 102277260

Inhaltsverzeichnis

Details

Erscheinungsjahr:	1997
Fachbereich:	Geometrie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 410 S. 29 s/w Illustr.
ISBN-13:	9780792342939
ISBN-10:	0792342933
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Parker, P. E. Dodson, C. T.
Hersteller:	Springer US Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 23 mm
Von/Mit:	P. E. Parker (u. a.)
Erscheinungsdatum:	31.01.1997
Gewicht:	0,639 kg