Characteristic Classes
eBook - PDF

Characteristic Classes

  1. 340 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Characteristic Classes

About this book

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds.



In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers.



Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

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Yes, you can access Characteristic Classes by John Milnor,James D. Stasheff in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebraic Geometry. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. §1. Smooth Manifolds
  7. §2. Vector Bundles
  8. §3. Constructing New Vector Bundles Out of Old
  9. §4. Stiefel-Whitney Classes
  10. §5. Grassmann Manifolds and Universal Bundles
  11. §6. A Cell Structure for Grassmann Manifolds
  12. §7. The Cohomology Ring H*(Gn; Z/2 )
  13. §8. Existence of Stiefel-Whitney Classes
  14. §9. Oriented Bundles and the Euler Class
  15. §10. The Thom Isomorphism Theorem
  16. §11. Computations in a Smooth Manifold
  17. §12. Obstructions
  18. §13. Complex Vector Bundles and Complex Manifolds
  19. §14. Chern Classes
  20. §15. Pontrjagin Classes
  21. §16. Chern Numbers and Pontrjagin Numbers
  22. §17. The Oriented Cobordism Ring Ω*
  23. §18. Thom Spaces and Transversality
  24. §19. Multiplicative Sequences and the Signature Theorem
  25. §20. Combinatorial Pontrjagin Classes
  26. Epilogue
  27. Appendix A: Singular Homology and Cohomology
  28. Appendix B: Bernoulli Numbers
  29. Appendix C: Connections, Curvature, and Characteristic Classes
  30. Bibliography
  31. Index