Differential Topology. (= Graduate Texts in Mathematics - Volume. 33).

Hirsch, Morris W.:

ISBN 10: 0387901485 / ISBN 13: 9780387901480

Edité par Springer, New York and Berlin, 1976

A propos de cet article

X, 221 pp. with some figures, Aus der Präsenzbibliothek eines Institutes, daher außergewöhnlich gut erhalten! (From the reference library of an institute, therefore exceptionally well preserved!) 0387901485 Sprache: Englisch Gewicht in Gramm: 540 Groß 8°, Original-Pappband (Hardcover), Bibliotheks-Exemplar (ordnungsgemäß entwidmet) mit Rückenschild, Stempel auf Titel, eingeschlagen, insgesamt gutes und innen sauberes Exemplar,(library copy in good condition),

N° de réf. du vendeur 123641

Détails bibliographiques

• Titre: Differential Topology. (= Graduate Texts in Mathematics - Volume. 33).
• Éditeur: Springer, New York and Berlin
• Date de parution: 1976
• Langue: anglais
• ISBN à 10 chiffres: 0387901485
• ISBN à 13 chiffres: 9780387901480
• Reliure: Couverture rigide
• Poids: 540 grammes
• Catalogues du vendeur:
  • Mathematik

A propos de ce titre

Synopsis

This book presents some of the basic topological ideas used in studying differentiable manifolds and maps. Mathematical prerequisites have been kept to a minimum; the standard course in analysis and general topology is adequate preparation. An appendix briefly summarizes some of the back- ground material. In order to emphasize the geometrical and intuitive aspects of differen- tial topology, I have avoided the use of algebraic topology, except in a few isolated places that can easily be skipped. For the same reason I make no use of differential forms or tensors. In my view, advanced algebraic techniques like homology theory are better understood after one has seen several examples of how the raw material of geometry and analysis is distilled down to numerical invariants, such as those developed in this book: the degree of a map, the Euler number of a vector bundle, the genus of a surface, the cobordism class of a manifold, and so forth. With these as motivating examples, the use of homology and homotopy theory in topology should seem quite natural. There are hundreds of exercises, ranging in difficulty from the routine to the unsolved. While these provide examples and further developments of the theory, they are only rarely relied on in the proofs of theorems.

Présentation de l'éditeur

This book gives the reader a thorough knowledge of the basic topological ideas necessary for studying differential manifolds. These topics include immersions and imbeddings, approach techniques, and the Morse classification of surfaces and their cobordism. The author keeps the mathematical prerequisites to a minimum; this and the emphasis on the geometric and intuitive aspects of the subject make the book an excellent and useful introduction for the student. There are numerous excercises on many different levels ranging from practical applications of the theorems to significant further development of the theory and including some open research problems.