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Algebraic topology --- 51 --- Mathematics --- 51 Mathematics --- Characteristic classes --- Fiber bundles (Mathematics) --- Foliations (Mathematics) --- Classes caractéristiques --- Faisceaux fibrés (Mathématiques) --- Feuilletages (mathématiques) --- Differential topology --- Topologie différentielle --- Feuilletages (mathématiques) --- Topologie différentielle --- Topologie differentielle --- Classes caracteristiques --- Espaces fibres --- Classes et nombres caracteristiques

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Differential topology --- 515.1 --- Topology --- 515.1 Topology --- Algebraic topology --- Homology theory --- Topologie algébrique --- Topologie différentielle --- Congresses --- Congrès --- Topologie différentielle --- Foliations (Mathematics) --- Feuilletages (mathématiques) --- Topologie différentielle. --- Feuilletages (mathématiques) --- Lie, Groupes de --- Topologie differentielle --- Classes caracteristiques --- Classes et nombres caracteristiques

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Ch. 1. Introduction -- Ch. 2. The Alternating Algebra -- Ch. 3. de Rham Cohomology -- Ch. 4. Chain Complexes and their Cohomology -- Ch. 5. The Mayer-Vietoris Sequence -- Ch. 6. Homotopy -- Ch. 7. Applications of de Rham Cohomology -- Ch. 8. Smooth Manifolds -- Ch. 9. Differential Forms on Smooth Manifolds -- Ch. 10. Integration on Manifolds -- Ch. 11. Degree, Linking Numbers and Index of Vector Fields -- Ch. 12. The Poincare-Hopf Theorem -- Ch. 13. Poincare Duality -- Ch. 14. The Complex Projective Space CP n -- Ch. 15. Fiber Bundles and Vector Bundles -- Ch. 16. Operations on Vector Bundles and their Sections -- Ch. 17. Connections and Curvature -- Ch. 18. Characteristic Classes of Complex Vector Bundles -- Ch. 19. The Euler Class -- Ch. 20. Cohomology of Projective and Grassmannian Bundles -- Ch. 21. Thom Isomorphism and the General Gauss-Bonnet Formula -- App. A. Smooth Partition of Unity -- App. B. Invariant Polynomials -- App. C. Proof of Lemmas 12.12 and 12.13 -- App. D. Exercises

Characteristic classes --- Classes caractéristiques --- Formes différentielles --- 514.74 --- Algebraic and analytic methods in geometry --- Characteristic classes. --- 514.74 Algebraic and analytic methods in geometry --- Classes caractéristiques --- Formes différentielles --- Differential forms --- Homology theory --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Forms, Differential --- Continuous groups --- Geometry, Differential --- Classes, Characteristic --- Differential topology --- Differential forms. --- Homology theory. --- Homologie --- Variétés différentiables --- Topologie differentielle --- Analyse sur une variété --- Classes et nombres caracteristiques

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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.

Algebraic topology --- Characteristic classes --- Classes caractéristiques --- 515.16 --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Classes, Characteristic --- Differential topology --- Topology of manifolds --- Characteristic classes. --- 515.16 Topology of manifolds --- Classes caractéristiques --- 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. --- Topologie differentielle --- Classes caracteristiques --- Classes et nombres caracteristiques