Characteristic Classes. (AM-76), Volume 76 / / John Milnor, James D. Stasheff

• Autore: Milnor John
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1974
• Descrizione fisica: 1 online resource (339 pages) : illustrations
• Disciplina: 514/.7
• Soggetto topico: Characteristic classes
• Soggetto non controllato: 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
• Persona (resp. second.): StasheffJames D.
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Characteristic Classes. (AM-76), Volume 76
• ISBN: 1-4008-8182-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154754803321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 76.; Princeton landmarks in mathematics and physics.