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The Topology of Fibre Bundles. (PMS-14), Volume 14 : Princeton Landmarks in Mathematics & Physics (Paperback) - Norman Steenrod

The Topology of Fibre Bundles. (PMS-14), Volume 14

Princeton Landmarks in Mathematics & Physics (Paperback)

Paperback Published: 25th April 1999
ISBN: 9780691005485
Number Of Pages: 224

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Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically.

It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.

The general theory of bundles
Introductionp. 3
Coordinate bundles and fibre bundlesp. 6
Construction of a bundle from coordinate transformationsp. 14
The product bundlep. 16
The Ehresmann-Feldbau definition of bundlep. 18
Differentiable manifolds and tensor bundlesp. 20
Factor spaces of groupsp. 28
The principal bundle and the principal mapp. 35
Associated bundles and relative bundlesp. 43
The induced bundlep. 47
Homotopies of maps of bundlesp. 49
Construction of cross-sectionsp. 54
Bundles having a totally disconnected groupp. 59
Covering spacesp. 67
The homotopy theory of bundles
Homotopy groupsp. 72
The operations of Pi1 on Pi np. 83
The homotopy sequence of a bundlep. 90
The classification of bundles over the n-spherep. 96
Universal bundles and the classification theoremp. 100
The fibering of spheres by spheresp. 105
The homotopy groups of spheresp. 110
Homotopy groups of the orthogonal groupsp. 114
A characteristic map for the bundle Rn+1 over S np. 118
A characteristic map for the bundle Un over S 2n - 1p. 124
The homotopy groups of miscellaneous manifoldsp. 131
Sphere bundles over spheresp. 134
The tangent bundle of S np. 140
On the non-existence of fiberings of spheres by spheresp. 144
The cohomology theory of bundles
The stepwise extension of a cross-sectionp. 148
Bundles of coefficientsp. 151
Cohomology groups based on a bundle of coefficientsp. 155
The obstruction cocyclep. 166
The difference cochainp. 169
Extension and deformation theoremsp. 174
The primary obstruction and the characteristic cohomology classp. 177
The primary difference of two cross-sectionsp. 181
Extensions of functions, and the homotopy classification of mapsp. 184
The Whitney characteristic classes of a sphere bundlep. 190
The Stiefel characteristic classes of differentiable manifoldsp. 199
Quadratic forms on manifoldsp. 204
Complex analytic manifolds and exterior forms of degree 2p. 209
Appendixp. 218
Bibliographyp. 223
Indexp. 228
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691005485
ISBN-10: 0691005486
Series: Princeton Landmarks in Mathematics & Physics (Paperback)
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 224
Published: 25th April 1999
Country of Publication: US
Dimensions (cm): 23.29 x 15.37  x 1.83
Weight (kg): 0.35

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