Characteristic Classes
James D. Stasheff, John Milnor
Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Stiefel–Whitney class, Principal ideal domain, Vector bundle, CW complex, Coefficient, Continuous function, Orthogonal group, Symmetric function, Eilenberg–Steenrod axioms, Gysin sequence, Fundamental class, Euler number, Canonical map, Existential quantification, Tangent bundle, Differentiable manifold, Isomorphism class, Open set, Axiom, Differential operator, Cohomology ring, Riemannian manifold, J-homomorphism, Polynomial, Variable (mathematics), Dimension, Levi-Civita connection, Homotopy, Complex manifold, Complex vector bundle, Thom space, K-theory, General linear group, Coordinate space, Equivalence class, Classifying space, Charles Ehresmann, Unit disk, Theorem, Grassmannian, Identity element, Diffeomorphism, Special case, Vector space, Homology (mathematics), Characteristic class, Dimension (vector space), Interior (topology), Chern class, Leibniz integral rule, Orthogonal complement, Fundamental group, Linear map, Topology, Smoothness, Cohomology, Compact space, Natural number, Steenrod algebra, Normal bundle, Orthonormal basis, Fiber bundle, Basis (linear algebra), De Rham cohomology, Subset, Cross product, Projection (mathematics), Euler class, Existence theorem, Subgroup