Introduction to Topological Manifolds (Graduate Texts in Mathematics) pdf epub mobi txt 電子書下載2025

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出版者:Springer

作者:John M. Lee

出品人:

頁數:402

译者:

出版時間:2000-05-25

價格:USD 44.95

裝幀:Paperback

isbn號碼:9780387950266

叢書系列:Graduate Texts in Mathematics

圖書標籤:

數學
拓撲流形
拓撲
Topology
流形
小徑分岔的花園
幾何
topology

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This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates, manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate mathematics education without ever hearing the word "manifold." Yet manifolds are part of the basic vocabulary of modern mathematics, and students need to know them as intimately as they know the integers, the real numbers, Euclidean spaces, groups, rings, and fields. In his beautifully conceived introduction, the author motivates the technical developments to follow by explaining some of the roles manifolds play in diverse branches of mathematics and physics. Then he goes on to introduce the basics of general topology and continues with the fundamental group, covering spaces, and elementary homology theory. Manifolds are introduced early and used as the main examples throughout. John M. Lee is currently Professor of Mathematics at the University of Washington.