Topology and Geometry

Glen E. Bredon

ISBN 10: 0387979263 / ISBN 13: 9780387979267

Edité par Springer, Humana, 1993

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - The golden age of mathematics-that was not the age of Euclid, it is ours. C. J. KEYSER This time of writing is the hundredth anniversary of the publication (1892) of Poincare's first note on topology, which arguably marks the beginning of the subject of algebraic, or 'combinatorial,' topology. There was earlier scattered work by Euler, Listing (who coined the word 'topology'), Mobius and his band, Riemann, Klein, and Betti. Indeed, even as early as 1679, Leibniz indicated the desirability of creating a geometry of the topological type. The establishment of topology (or 'analysis situs' as it was often called at the time) as a coherent theory, however, belongs to Poincare. Curiously, the beginning of general topology, also called 'point set topology,' dates fourteen years later when Frechet published the first abstract treatment of the subject in 1906. Since the beginning of time, or at least the era of Archimedes, smooth manifolds (curves, surfaces, mechanical configurations, the universe) have been a central focus in mathematics. They have always been at the core of interest in topology. After the seminal work of Milnor, Smale, and many others, in the last half of this century, the topological aspects of smooth manifolds, as distinct from the differential geometric aspects, became a subject in its own right.

N° de réf. du vendeur 9780387979267

Détails bibliographiques

• Titre: Topology and Geometry
• Éditeur: Springer, Humana
• Date de parution: 1993
• Langue: anglais
• ISBN à 10 chiffres: 0387979263
• ISBN à 13 chiffres: 9780387979267
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 37 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 37 millimètres de profondeur
• Poids: 1027 grammes

A propos de ce titre

Synopsis

This book is intended as a textbook for a first-year graduate course on algebraic topology, with as strong flavoring in smooth manifold theory. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. It covers most of the topics all topologists will want students to see, including surfaces, Lie groups and fibre bundle theory.

Présentation de l'éditeur

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics" - MATHEMATICAL REVIEWS