纤维丛拓扑学

作者简介

本书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。目次：丛的广义理论；丛的同伦理论；丛的上同调理论。

书籍目录

Part I.THE GENERAL THEORY OF BUNDLES1.Introduction2.Coordinate bundles and fibre bundles3.Construction of a bundle from coordinate transformations4.The product bundle5.The Ehresmann-Feldbau definition of bundle6.Differentiable manifolds and tensor bundles7.Factor spaces of groups8.The principal bundle and the principal map9.Associated bundles and relative bundles10.The induced bundle11.Homotopies of maps of bundles12.Construction of cross-sections13.Bundles having a totally disconnected group14.Covering spacesPart II.THE HOMOTOPY THEORY OF BUNDLES15.Homotopy groups16.The operations of π1 on π217.The homotopy; sequence of a bundle18.The classification of bundles over the n-sphere19.Universal bundles and the classification theorem.20.The fibering of spheres by spheres21.The homotopy groups of spheres22.Homotopy groups of the orthogonal groups23.A characteristic map for the bundle Rn+l over Sn24.A characteristic map for the bundle Un over S2n-125.The homotopy groups of miscellaneous manifolds26.Sphere bundles over spheres27.The tangent bundle of Sn28.On the non-existence of fiberings of spheres by spheresPart III.THE COHOMOLOGY THEORY OF BUNDLES29.The stepwise extension of a cross-section30.Bundles of coefficients31.Cohomology groups based on a bundle of coefficients32.The obstruction cocycle33.The difference cochain34.Extension and deformation theorems35.The primary obstruction and the characteristic cohomology, class36.The primary difference of two cross-sections37.Extensions of functions, and the homotopy classification of maps38.The Whitney characteristic classes of a sphere bundle39.The Stiefel characteristic classes of differentiable manifolds40.Quadratic forms on manifolds41.Complex analytic manifolds and exterior forms of degree 2AppendixBibliographyIndex

图书封面

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