Characteristic Classes. (AM-76), Volume 76 /

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, t...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Milnor, John (Autor), Stasheff, James D. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2016]
Colección:Annals of Mathematics Studies ; 76
Temas:
Characteristic classes.
MATHEMATICS / Topology.
Additive group.
Axiom.
Basis (linear algebra).
Boundary (topology).
Bundle map.
CW complex.
Canonical map.
Cap product.
Cartesian product.
Characteristic class.
Charles Ehresmann.
Chern class.
Classifying space.
Coefficient.
Cohomology ring.
Cohomology.
Compact space.
Complex dimension.
Complex manifold.
Complex vector bundle.
Complexification.
Computation.
Conformal geometry.
Continuous function.
Coordinate space.
Cross product.
De Rham cohomology.
Diffeomorphism.
Differentiable manifold.
Differential form.
Differential operator.
Dimension (vector space).
Dimension.
Direct sum.
Directional derivative.
Eilenberg-Steenrod axioms.
Embedding.
Equivalence class.
Euler class.
Euler number.
Existence theorem.
Existential quantification.
Exterior (topology).
Fiber bundle.
Fundamental class.
Fundamental group.
General linear group.
Grassmannian.
Gysin sequence.
Hausdorff space.
Homeomorphism.
Homology (mathematics).
Homotopy.
Identity element.
Integer.
Interior (topology).
Isomorphism class.
J-homomorphism.
K-theory.
Leibniz integral rule.
Levi-Civita connection.
Limit of a sequence.
Linear map.
Metric space.
Natural number.
Natural topology.
Neighbourhood (mathematics).
Normal bundle.
Open set.
Orthogonal complement.
Orthogonal group.
Orthonormal basis.
Partition of unity.
Permutation.
Polynomial.
Power series.
Principal ideal domain.
Projection (mathematics).
Representation ring.
Riemannian manifold.
Sequence.
Singular homology.
Smoothness.
Special case.
Steenrod algebra.
Stiefel-Whitney class.
Subgroup.
Subset.
Symmetric function.
Tangent bundle.
Tensor product.
Theorem.
Thom space.
Topological space.
Topology.
Unit disk.
Unit vector.
Variable (mathematics).
Vector bundle.
Vector space.
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Tabla de Contenidos:
  • Frontmatter
  • Preface
  • Contents
  • §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 Pontrjagin Numbers
  • §17. The Oriented Cobordism Ring Ω*
  • §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
  • Bibliography
  • Index

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