The Topology of Stiefel Manifolds

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Cambridge University Press, 1976 - Mathematics - 168 pages
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Stiefel manifolds are an interesting family of spaces much studied by algebraic topologists. These notes, which originated in a course given at Harvard University, describe the state of knowledge of the subject, as well as the outstanding problems. The emphasis throughout is on applications (within the subject) rather than on theory. However, such theory as is required is summarized and references to the literature are given, thus making the book accessible to non-specialists and particularly graduate students. Many examples are given and further problems suggested.
  

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Contents

algebra versus topology
1
The Stiefel manifolds
13
The auxiliary spaces
21
Retractible fibrations
27
Thom spaces
33
Homotopy equivariance
40
Crosssections and the Stype
45
Relative Stiefel manifolds
52
Samelson products
94
The Hopf construction
100
The Bott suspension
109
The intrinsic join again
116
Homotopycommutativity
123
The triviality problem
129
When is P neutral?
133
When is V neutral?
139

Cannibalistic characteristic classes
57
Exponential characteristic classes
62
The main theorem of Jtheory
71
The fibre suspension
78
Canonical automorphisms
83
The iterated suspension
89
n
146
Further results and problems
150
Bibliography
155
Index
167
Copyright

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Page 155 - WD Barcus and MG Barratt, On the homotopy classification of the extensions of a fixed map, Trans. Amer. Math. Soc. 88 ( 1958), 57-74.

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About the author (1976)

James, University of Oxford, UK.

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