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OverviewBased on lectures given by the authors at Moscow and Leningrad Universities, this textbook gives a systematic exposition of the main parts of Topology: Homology, Homotopy, Fibre Bundles, and Smooth Manifolds.The main purpose is to present all parts of topology as a unified whole. As a methodological innovation a coordinateless approach to the theory of fibre bundles and an exposition of the foundation of differerential topology without use of differential equations is presented. Many descriptive examples and drawings are included; each section is followed by a set of well chosen exercises. The reader needs only a basic knowledge of set theory, algebra and calculus; so first-year graduate students will find a thorough a profound introduction into the advanced theory of Differential Manifolds. Full Product DetailsAuthor: D. B. Fuks , A. Iacob , V. A. RokhlinPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 1st ed. 1984. 2nd printing 2004 Dimensions: Width: 15.50cm , Height: 2.70cm , Length: 23.50cm Weight: 1.640kg ISBN: 9783540135777ISBN 10: 3540135774 Pages: 520 Publication Date: 01 August 1984 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: Out of print, replaced by POD  We will order this item for you from a manufatured on demand supplier. Table of ContentsSet-Theoretical Terms and Notations Used in This Book, but not Generally Adopted.- 1 Topological Spaces.- § 1. Fundamental Concepts.- §2. Constructions.- §3. Homotopies.- 2 Cellular Spaces.- §1. Cellular Spaces and Their Topological Properties.- §2. Simplicial Spaces.- §3. Homotopy Properties of Cellular Spaces.- 3 Smooth Manifolds.- §1. Fundamental Concepts.- §2. Stiefel and Grassman Manifolds.- §3. A Digression: Three Theorems from Calculus.- §4. Embeddings. Immersions. Smoothings. Approximations.- §5. The Simplest Structure Theorems.- 4 Bundles.- §1. Bundles without Group Structure.- §2. A Digression: Topological Groups and Transformation Groups.- §3. Bundles with a Group Structure.- §4. The Classification of Steenrod Bundles.- §5. Vector Bundles.- §6. Smooth Bundles.- 5 Homotopy Groups.- §1. The General Theory.- §2. The Homotopy Groups of Spheres and of Classical Manifolds.- §3. Homotopy Groups of Cellular Spaces.- §4. Weak Homotopy Equivalence.- §5. The Whitehead Product.- §6. Continuation of the Theory of Bundles.- Glossary of Symbols.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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