| 书目名称 | Introduction to Geometry and Topology | | 编辑 | Werner Ballmann | | 视频video | | | 概述 | Lecture-tested introduction to topology, differential topology, and differential geometry.Contributes to a wide range of topics on a few pages.About 70 exercises motivate the application of the learne | | 丛书名称 | Compact Textbooks in Mathematics | | 图书封面 |  | | 描述 | .This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems.. . The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes‘s integral formula.. . The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential | | 出版日期 | Textbook 20181st edition | | 关键词 | field; cohomology; curvature; curv; Liesche Group; plurality; context | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-0983-2 | | isbn_softcover | 978-3-0348-0982-5 | | isbn_ebook | 978-3-0348-0983-2Series ISSN 2296-4568 Series E-ISSN 2296-455X | | issn_series | 2296-4568 | | copyright | Springer Basel 2018 |
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发表于 2025-3-21 17:45:40
