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LECTURES ON ALGEBRAIC TOPOLOGYPDF|Epub|txt|kindle电子书版本下载
![LECTURES ON ALGEBRAIC TOPOLOGY](https://www.shukui.net/cover/59/34199532.jpg)
- 著
- 出版社: EUROPEAN MATHEMATICAL SOCIETY
- ISBN:303719023X
- 出版时间:2006
- 标注页数:99页
- 文件大小:17MB
- 文件页数:105页
- 主题词:
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图书目录
1 Elements of homology theory1
1.1 Categories and functors1
1.2 Some geometric properties of RN4
1.3 Chain complexes7
1.4 Homology groups of a simplicial complex10
1.5 Simplicial maps13
1.6 Induced homomorphisms of homology groups17
1.7 Degrees of maps between manifolds18
1.8 Applications of the degree of a map23
1.9 Relative homology32
1.10 The exact homology sequence33
1.11 Axiomatic point of view on homology37
1.12 Digression to the theory of Abelian groups39
1.13 Calculation of homology groups41
1.14 Cellular homology43
1.15 Lefschetz fixed point theorem47
1.16 Homology with coefficients50
1.17 Elements of cohomology theory53
1.18 The Poincare duality58
2 Elements of homotopy theory61
2.1 Definition of the fundamental group61
2.2 Independence of the choice of the base point63
2.3 Presentations of groups65
2.4 Calculation of fundamental groups68
2.5 Wirtinger's presentation72
2.6 The higher homotopy groups74
2.7 Bundles and exact sequences76
2.8 Coverings79
Answers, hints, solutions83
Bibliography95
Index97