数学经典教材：纤维丛拓扑学（英文影印版）
作 者： （美）斯廷罗德（Steenrod，N.） 著
出版时间：2011
丛编项： 纤维丛拓扑学
内容简介
《数学经典教材：纤维丛拓扑学（影印版）》是一部系统讲述纤维丛拓扑学的专著，是首次对该科目进行系统介绍的入门书籍。纤维丛作为微分几何的不可缺少的一部分，在现代物理中的具有相当重要的位置。书中从纤维丛的介绍开始，包括微分流形和覆盖面，接着讲述更深层次的话题，如同调，上同调理论，以及纤维丛的更深层次的性质。对于想要深入全面地学习纤维丛的读者，本书十分合适。
目录
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
