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Topology and Geometry

1st Corrected ed. 2002. Corr. 3rd printing 1997. Book. Sprache: Englisch.
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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 … weiterlesen
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Produktdetails

Titel: Topology and Geometry
Autor/en: Glen E. Bredon

ISBN: 0387979263
EAN: 9780387979267
1st Corrected ed. 2002. Corr. 3rd printing 1997.
Book.
Sprache: Englisch.
Springer New York

17. Oktober 1997 - gebunden - 580 Seiten

Beschreibung

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.

Inhaltsverzeichnis

Preface; 1. General Topology; 2. Diferentiable Manifolds; 3. Fundamental Group; 4. Homology Theory; 5. Cohomology; 6. Products and Duality; 7. Homotopy Theory; Appendices A-E; Bibliography; Index of Symbols; Index

Pressestimmen

G.E. Bredon
Topology and Geometry
"An interesting and original graduate text in topology and geometry. The topics covered include . . . general topology, smooth manifolds, homology and homotopy groups, duality, cohomology and products . . . a good lecturer can use this text to create a fine course at the appropriate level . . . There are various innovative things, which are accessible but not traditionally covered. A beginning graduate student can use this text to learn a great deal of mathematics."-MATHEMATICAL REVIEWS

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