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Cover: 9781441931030 | Topology and Geometry | Glen E. Bredon | Taschenbuch | Paperback | XIV
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Topology and Geometry
Taschenbuch von Glen E. Bredon
Sprache: Englisch

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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.
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.
Zusammenfassung
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.
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
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xiv
557 S.
85 s/w Illustr.
ISBN-13: 9781441931030
ISBN-10: 1441931031
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Bredon, Glen E.
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 32 mm
Von/Mit: Glen E. Bredon
Erscheinungsdatum: 19.11.2010
Gewicht: 0,867 kg
Artikel-ID: 107219384
Zusammenfassung
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.
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
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xiv
557 S.
85 s/w Illustr.
ISBN-13: 9781441931030
ISBN-10: 1441931031
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Bredon, Glen E.
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 32 mm
Von/Mit: Glen E. Bredon
Erscheinungsdatum: 19.11.2010
Gewicht: 0,867 kg
Artikel-ID: 107219384
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