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    Characteristic Classes. (AM-76), Volume 76

    Characteristic Classes. (AM-76), Volume 76

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    Bog E-bog
    • Format
    • Bog, paperback
    • Engelsk

    Beskrivelse

    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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    K-theory Topology Dimension Steenrod algebra Chern class Continuous function Orthogonal group Vector bundle Characteristic class Fiber bundle CW complex Polynomial Classifying space Differentiable manifold Riemannian manifold Existence theorem Cohomology Theorem Diffeomorphism Compact space Smoothness Homotopy De Rham cohomology Tangent bundle Vector space Axiom Complex manifold Orthonormal basis Eilenberg-Steenrod axioms Coefficient General Linear Group Basis (linear algebra) Canonical map Complex vector bundle Dimension (vector space) Coordinate Space Euler number Euler class Charles Ehresmann Cohomology ring Existential quantification Fundamental class equivalence class Cross product Homology (mathematics) differential operator Identity element Isomorphism class Leibniz integral rule Grassmannian Fundamental group Natural Number Open Set Orthogonal complement Normal bundle Gysin sequence Principal Ideal Domain Interior (topology) Linear map subgroup symmetric function Thom space Variable (mathematics) J-homomorphism Projection (mathematics) Unit Disk Stiefel–Whitney class Subset Special case
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