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Graduate Texts in Mathematics #139: Topology and Geometryby Glen E. Bredon
Synopses & ReviewsPublisher Comments:This book is intended as a textbook for a firstyear 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. With a thoroughly modern point of view, it is the first truly new textbook in topology since Spanier, almost 25 years ago. Although the book is comprehensive, there is no attempt made to present the material in excessive generality, except where generality improves the efficiency and clarity of the presentation.
Book News Annotation:Intended as a textbook for a firstyear graduate course on algebraic topology, with a strong flavoring in smooth manifold theory. Starting with general topology, discusses differential manifolds, cohomology, products and duality, the fundamental group, homology theory, homeotropy theory, surfaces, Lie groups, and baby bundle theory. Problems follow each section.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis: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
Table of ContentsPreface; 1. General Topology; 2. Diferentiable Manifolds; 3. Fundamental Group; 4. Homology Theory; 5. Cohomology; 6. Products and Duality; 7. Homotopy Theory; Appendices AE; Bibliography; Index of Symbols; Index
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