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Vector bundles - Vol 1

Vector bundles. --- Characteristic classes. --- Fibrés vectoriels --- Classes caractéristiques --- 514.76 --- Characteristic classes --- Vector Bundles --- Fiber spaces (Mathematics) --- Classes, Characteristic --- Differential topology --- Geometry of differentiable manifolds and of their submanifolds --- 514.76 Geometry of differentiable manifolds and of their submanifolds

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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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Characteristic classes --- Classes caractéristiques --- Characteristic classes. --- Foliations (Mathematics). --- Classes caractéristiques --- Foliations (Mathematics) --- 515.16 --- Foliated structures --- Differential topology --- 515.16 Topology of manifolds --- Topology of manifolds --- Classes, Characteristic --- Topologie différentielle --- Feuilletages (mathématiques) --- Topologie différentielle --- Feuilletages (mathématiques) --- Topologie differentielle --- Algebres de lie --- Classes et nombres caracteristiques --- Cohomologie

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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