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拓?fù)淞餍我?: 第2版 版權(quán)信息
- ISBN：9787519276089
- 條形碼：9787519276089 ; 978-7-5192-7608-9
- 裝幀：簡(jiǎn)裝本
- 冊(cè)數(shù)：暫無(wú)
- 重量：暫無(wú)
- 所屬分類：>>
拓?fù)淞餍我?: 第2版 本書特色
拓?fù)淞餍问菙?shù)學(xué)的一個(gè)很重要的分支，每個(gè)學(xué)習(xí)數(shù)學(xué)的同學(xué)和老師都值得擁有這樣一部經(jīng)典教材。
拓?fù)淞餍我?: 第2版 內(nèi)容簡(jiǎn)介
本書作者是美國(guó)華盛頓大學(xué)教授，具有豐富的教學(xué)經(jīng)驗(yàn), 他在華盛頓大學(xué)和哈佛大學(xué)教授流形課程已有15年之久。書中論述了流形理論中所需的拓?fù)鋵W(xué)基本概念，特別是微分幾何、代數(shù)幾何和相關(guān)領(lǐng)域。線和曲面；同倫和基本群論；圓和球；群論；Seifert-Van Kampen定理；覆蓋空間；覆蓋類別；同調(diào)。
讀者對(duì)象：數(shù)學(xué)、理論物理專業(yè)的高年級(jí)本科生、研究生以及相關(guān)的科研人員。
拓?fù)淞餍我?: 第2版 目錄
Preface
1 Introduction
What Are Manifolds
Why Study Manifolds
2 Topological Spaces
Topologies
Convergence and Continuity
Hausdorff Spaces
Bases and Countability
Manifolds
Problems
3 New Spaces from Old
Subspaces
Product Spaces
Disjoint Union Spaces
Quotient Spaces
Adjunction Spaces
Topological Groups and Group Actions
Problems
4 Connectedness and Compactness
Connectedness
Compactness
Local Compactness
Paracompactness
Proper Maps
Problems
5 Cell Complexes
Cell Complexes and CW Complexes
Topological Properties of Cw Complexes
Classification of 1-Dimensional Manifold
Simplicial Complexes
Problems
6 Compact Surfaces
Surfaces
Connected Sums of Surfaces
Polygonal Presentations of Surfaces
The Classification Theorem
The Euler Characteristic
Orientability
Problems
7 Homotopy and the Fundamental Group
Homotopy
The Fundamental Group
Homomorphisms Induced by Continuous Maps
Homotopy Equivalence
Higher Homotopy Groups
Categories and Functors
Problems
8 The Circle
Lifting Properties of the Circle
1 Introduction
What Are Manifolds
Why Study Manifolds
2 Topological Spaces
Topologies
Convergence and Continuity
Hausdorff Spaces
Bases and Countability
Manifolds
Problems
3 New Spaces from Old
Subspaces
Product Spaces
Disjoint Union Spaces
Quotient Spaces
Adjunction Spaces
Topological Groups and Group Actions
Problems
4 Connectedness and Compactness
Connectedness
Compactness
Local Compactness
Paracompactness
Proper Maps
Problems
5 Cell Complexes
Cell Complexes and CW Complexes
Topological Properties of Cw Complexes
Classification of 1-Dimensional Manifold
Simplicial Complexes
Problems
6 Compact Surfaces
Surfaces
Connected Sums of Surfaces
Polygonal Presentations of Surfaces
The Classification Theorem
The Euler Characteristic
Orientability
Problems
7 Homotopy and the Fundamental Group
Homotopy
The Fundamental Group
Homomorphisms Induced by Continuous Maps
Homotopy Equivalence
Higher Homotopy Groups
Categories and Functors
Problems
8 The Circle
Lifting Properties of the Circle
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