| |
Based on lectures given by J. W. Milnor at Princeton in 1957, and written up by J.D. Stasheff a decade later, this book is widely recognised as a classic. It remains the best introduction to the algebraic topology of vector bundles, more specifically to the "characteristic classes" associated with the names of Euler, Stiefel and Whitney, Chern, and Pontryagin. The book also contains a lovely treatment of Thom’s cobordism theory, and the Appendices give brisk accounts of singular homology and cohomology, as well as the Chern-Weil Theory.
Milnor was awarded the Fields Medal in 1962 and the Steele Prize for Mathematical Exposition in 2004. A part of the citation for the Steele Prize says:
The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor’s writings, whether they be research or expository. Reading his books, one is struck with the ease with which the subject is unfolding, and it only becomes apparent after reflection that this ease is the mark of a master.
Contents: Preface 1. Smooth Manifolds 2. Vector Bundles 3. Constructing New Vector Bundles Out of Old 4. Stiefel-Whitney Classes 5. Grassmann Manifolds and Universal Bundles 6. A Cell Structure for Grassmann Manifolds 7. The Cohomology Ring H*(Gn; Z/2) 8. Existence of Stiefel-Whitney Classes 9. Oriented Bundles and the Euler Class 10.The Thom Isomorphism Theorem 11.Computations in a Smooth Manifold 12. Obstructions 13. Complex Vector Bundles and Complex Manifolds 14. Chern Classes 15. Pontrjagin Classes 16. Chern Numbers and Pontragin Numbers 17. The Oriented Cobordism Ring W 18. Thom Spaces and Transversality 19. Multiplicative Sequences and the Signature Theorem 20. Combinatorial Pontrjagin Classes. Epilogue.
Appendix A: Singular Homology and Cohomology. Appendix B: Bernoulli Numbers. Appendix C: Connections, Curvature, and characteristic Classes.
ISBN - 8185931526
|
| |
Pages : 342
|