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Fibrewise Homotopy Theory By Michael Charles Crabb

Fibrewise Homotopy Theory by Michael Charles Crabb

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Summary

Topology occupies a central position in modern mathematics, and the concept of the fibre bundle provides an appropriate framework for studying differential geometry. Fibrewise homotopy theory is a very large subject that has attracted a good deal of research in recent years. This book provides an overview of the subject as it stands at present.

Fibrewise Homotopy Theory Summary

Fibrewise Homotopy Theory by Michael Charles Crabb

Topology occupies a central position in modern mathematics, and the concept of the fibre bundle provides an appropriate framework for studying differential geometry. Fibrewise homotopy theory is a very large subject that has attracted a good deal of research in recent years. This book provides an overview of the subject as it stands at present.

Table of Contents

I. A Survey of Fibrewise Homotopy Theory.- 1: An Introduction to Fibrewise Homotopy Theory.- 1. Fibrewise spaces.- 2. Fibrewise transformation groups.- 3. Fibrewise homotopy.- 4. Fibrewise cofibrations.- 5. Fibrewise fibrations.- 6. Numerable coverings.- 7. Fibrewise fibre bundles.- 8. Fibrewise mapping-spaces.- 2: The Pointed Theory.- 9. Fibrewise pointed spaces.- 10. Fibrewise one-point (Alexandroff) compactification.- 11. Fibrewise pointed homotopy.- 12. Fibrewise pointed cofibrations.- 13. Fibrewise pointed fibrations.- 14. Numerable coverings (continued).- 15. Fibrewise pointed mapping-spaces.- 16. Fibrewise well-pointed and fibrewise non-degenerate spaces.- 17. Fibrewise complexes.- 18. Fibrewise Whitehead products.- 3: Applications.- 19. Numerical invariants.- 20. The reduced product (James) construction.- 21. Fibrewise Hopf and coHopf structures.- 22. Fibrewise manifolds.- 23. Fibrewise configuration spaces.- II. An Introduction to Fibrewise Stable Homotopy Theory.- 1: Foundations.- 1. Fibre bundles.- 2. Complements on homotopy theory.- 3. Stable homotopy theory.- 4. The Euler class.- 2: Fixed-point Methods.- 5. Fibrewise Euclidean and Absolute Neighbourhood Retracts.- 6. Lefschetz fixed-point theory for fibrewise ENRs.- 7. Fixed-point theory for fibrewise ANRs.- 8. Virtual vector bundles and stable spaces.- 9. The Adams conjecture.- 10. Duality.- 3: Manifold Theory.- 11. Fibrewise differential topology.- 12. The Pontrjagin-Thom construction.- 13. Miller's stable splitting of U(n).- 14. Configuration spaces and splittings.- 4: Homology Theory.- 15. Fibrewise homology.- References.

Additional information

NLS9781447112679
9781447112679
1447112679
Fibrewise Homotopy Theory by Michael Charles Crabb
New
Paperback
Springer London Ltd
2011-12-16
341
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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