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[文献] Geometry and Topology of Manifolds: Surfaces and Beyond [推广有奖]

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北固隐 学生认证  发表于 2020-11-18 14:35:17 |AI写论文
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Geometry and Topology of Manifolds: Surfaces and Beyond

https://bookstore.ams.org/gsm-208

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This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usu ...
关键词:manifolds Topology Manifold Surfaces Geometry

沙发
nivastuli 在职认证  发表于 2020-11-18 14:35:18
This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.
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藤椅
北固隐 学生认证  发表于 2021-2-27 13:29:46
nivastuli 发表于 2020-11-18 14:35
This book represents a novel approach to differential topology. Its main focus is to give a comprehe ...
抱歉……现在才看到
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板凳
三江鸿 发表于 2022-4-18 10:28:44 来自手机
感谢沙发分享

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giresse 在职认证  发表于 2022-4-18 23:14:47
nivastuli 发表于 2020-11-18 14:35
This book represents a novel approach to differential topology. Its main focus is to give a comprehe ...

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