1.

Record Nr.

UNINA9910299968503321

Autore

Weintraub Steven H

Titolo

Fundamentals of Algebraic Topology / / by Steven H. Weintraub

Pubbl/distr/stampa

New York, NY : , : Springer New York : , : Imprint : Springer, , 2014

ISBN

1-4939-1844-3

Edizione

[1st ed. 2014.]

Descrizione fisica

1 online resource (X, 163 p. 82 illus.)

Collana

Graduate Texts in Mathematics, , 0072-5285 ; ; 270

Disciplina

514.2

Soggetti

Algebraic topology

Manifolds (Mathematics)

Complex manifolds

Category theory (Mathematics)

Homological algebra

Algebraic Topology

Manifolds and Cell Complexes (incl. Diff.Topology)

Category Theory, Homological Algebra

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Preface -- 1. The Basics -- 2. The Fundamental Group -- 3. Generalized Homology Theory -- 4. Ordinary Homology Theory -- 5. Singular Homology Theory -- 6. Manifolds -- 7. Homotopy Theory -- 8. Homotopy Theory -- A. Elementary Homological Algebra -- B. Bilinear Forms.- C. Categories and Functors -- Bibliography -- Index.

Sommario/riassunto

This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and



manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography.