《纖維叢拓撲學》是2011年1月由世界圖書出版公司出版的圖書，作者是Norman Steenrod。本書系統地講述了纖維叢拓撲學等入門知識和深入研究。
基本介紹
- 書名：纖維叢拓撲學
- 又名：The Topology of Fibre Bundles
- 作者：Norman Steenrod
- ISBN：9787510029561
- 頁數：229
- 定價：35.00元
- 出版社：世界圖書出版公司
- 出版時間：2011-1
- 裝幀：平裝
- 開本：24開
內容簡介,圖書目錄,
內容簡介
《數學經典教材：纖維叢拓撲學（影印版）》是一部系統講述纖維叢拓撲學的專著，是首次對該科目進行系統介紹的入門書籍。纖維叢作為微分幾何的不可缺少的一部分，在現代物理中的具有相當重要的位置。書中從纖維叢的介紹開始，包括微分流形和覆蓋面，接著講述更深層次的話題，如同調，上同調理論，以及纖維叢的更深層次的性質。
圖書目錄
Part I.THE GENERAL THEORY OF BUNDLES
1.Introduction
2.Coordinate bundles and fibre bundles
3.Construction of a bundle from coordinate transformations
4.The product bundle
5.The Ehresmann-Feldbau definition of bundle
6.Differentiable manifolds and tensor bundles
7.Factor spaces of groups
8.The principal bundle and the principal map
9.Associated bundles and relative bundles
10.The induced bundle
11.Homotopies of maps of bundles
12.Construction of cross-sections
13.Bundles having a totally disconnected group
14.Covering spaces
Part II.THE HOMOTOPY THEORY OF BUNDLES
15.Homotopy groups
16.The operations of π1 on π2
17.The homotopy; sequence of a bundle
18.The classification of bundles over the n-sphere
19.Universal bundles and the classification theorem.
20.The fibering of spheres by spheres
21.The homotopy groups of spheres
22.Homotopy groups of the orthogonal groups
23.A characteristic map for the bundle Rn+l over Sn
24.A characteristic map for the bundle Un over S2n-1
25.The homotopy groups of miscellaneous manifolds
26.Sphere bundles over spheres
27.The tangent bundle of Sn
28.On the non-existence of fiberings of spheres by spheres
Part III.THE COHOMOLOGY THEORY OF BUNDLES
29.The stepwise extension of a cross-section
30.Bundles of coefficients
31.Cohomology groups based on a bundle of coefficients
32.The obstruction cocycle
33.The difference cochain
34.Extension and deformation theorems
35.The primary obstruction and the characteristic cohomology, class
36.The primary difference of two cross-sections
37.Extensions of functions, and the homotopy classification of maps
38.The Whitney characteristic classes of a sphere bundle
39.The Stiefel characteristic classes of differentiable manifolds
40.Quadratic forms on manifolds
41.Complex analytic manifolds and exterior forms of degree 2
Appendix
Bibliography
Index
1.Introduction
2.Coordinate bundles and fibre bundles
3.Construction of a bundle from coordinate transformations
4.The product bundle
5.The Ehresmann-Feldbau definition of bundle
6.Differentiable manifolds and tensor bundles
7.Factor spaces of groups
8.The principal bundle and the principal map
9.Associated bundles and relative bundles
10.The induced bundle
11.Homotopies of maps of bundles
12.Construction of cross-sections
13.Bundles having a totally disconnected group
14.Covering spaces
Part II.THE HOMOTOPY THEORY OF BUNDLES
15.Homotopy groups
16.The operations of π1 on π2
17.The homotopy; sequence of a bundle
18.The classification of bundles over the n-sphere
19.Universal bundles and the classification theorem.
20.The fibering of spheres by spheres
21.The homotopy groups of spheres
22.Homotopy groups of the orthogonal groups
23.A characteristic map for the bundle Rn+l over Sn
24.A characteristic map for the bundle Un over S2n-1
25.The homotopy groups of miscellaneous manifolds
26.Sphere bundles over spheres
27.The tangent bundle of Sn
28.On the non-existence of fiberings of spheres by spheres
Part III.THE COHOMOLOGY THEORY OF BUNDLES
29.The stepwise extension of a cross-section
30.Bundles of coefficients
31.Cohomology groups based on a bundle of coefficients
32.The obstruction cocycle
33.The difference cochain
34.Extension and deformation theorems
35.The primary obstruction and the characteristic cohomology, class
36.The primary difference of two cross-sections
37.Extensions of functions, and the homotopy classification of maps
38.The Whitney characteristic classes of a sphere bundle
39.The Stiefel characteristic classes of differentiable manifolds
40.Quadratic forms on manifolds
41.Complex analytic manifolds and exterior forms of degree 2
Appendix
Bibliography
Index
