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Summary
Author Biography
Table of Contents
The general theory of bundles | |
Introduction | p. 3 |
Coordinate bundles and fibre bundles | p. 6 |
Construction of a bundle from coordinate transformations | p. 14 |
The product bundle | p. 16 |
The Ehresmann-Feldbau definition of bundle | p. 18 |
Differentiable manifolds and tensor bundles | p. 20 |
Factor spaces of groups | p. 28 |
The principal bundle and the principal map | p. 35 |
Associated bundles and relative bundles | p. 43 |
The induced bundle | p. 47 |
Homotopies of maps of bundles | p. 49 |
Construction of cross-sections | p. 54 |
Bundles having a totally disconnected group | p. 59 |
Covering spaces | p. 67 |
The homotopy theory of bundles | |
Homotopy groups | p. 72 |
The operations of Pi1 on Pi n | p. 83 |
The homotopy sequence of a bundle | p. 90 |
The classification of bundles over the n-sphere | p. 96 |
Universal bundles and the classification theorem | p. 100 |
The fibering of spheres by spheres | p. 105 |
The homotopy groups of spheres | p. 110 |
Homotopy groups of the orthogonal groups | p. 114 |
A characteristic map for the bundle Rn+1 over S n | p. 118 |
A characteristic map for the bundle Un over S 2n - 1 | p. 124 |
The homotopy groups of miscellaneous manifolds | p. 131 |
Sphere bundles over spheres | p. 134 |
The tangent bundle of S n | p. 140 |
On the non-existence of fiberings of spheres by spheres | p. 144 |
The cohomology theory of bundles | |
The stepwise extension of a cross-section | p. 148 |
Bundles of coefficients | p. 151 |
Cohomology groups based on a bundle of coefficients | p. 155 |
The obstruction cocycle | p. 166 |
The difference cochain | p. 169 |
Extension and deformation theorems | p. 174 |
The primary obstruction and the characteristic cohomology class | p. 177 |
The primary difference of two cross-sections | p. 181 |
Extensions of functions, and the homotopy classification of maps | p. 184 |
The Whitney characteristic classes of a sphere bundle | p. 190 |
The Stiefel characteristic classes of differentiable manifolds | p. 199 |
Quadratic forms on manifolds | p. 204 |
Complex analytic manifolds and exterior forms of degree 2 | p. 209 |
Appendix | p. 218 |
Bibliography | p. 223 |
Index | p. 228 |
Table of Contents provided by Publisher. All Rights Reserved. |
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