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100   $a20190708d2016      fg 
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aCharacteristic Classes. (AM-76), Volume 76 /$fJohn Milnor, James D. Stasheff
210  1$aPrinceton, NJ :$cPrinceton University Press,$d[2016]
210  4$d©1974
215   $a1 online resource (339 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v246
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08122-0 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter --$tPreface --$tContents --$t§1. Smooth Manifolds --$t§2. Vector Bundles --$t§3. Constructing New Vector Bundles Out of Old --$t§4. Stiefel-Whitney Classes --$t§5. Grassmann Manifolds and Universal Bundles --$t§6. A Cell Structure for Grassmann Manifolds --$t§7. The Cohomology Ring H*(Gn; Z/2) --$t§8. Existence of Stiefel-Whitney Classes --$t§9. Oriented Bundles and the Euler Class --$t§10. The Thom Isomorphism Theorem --$t§11. Computations in a Smooth Manifold --$t§12. Obstructions --$t§13. Complex Vector Bundles and Complex Manifolds --$t§14. Chern Classes --$t§15. Pontrjagin Classes --$t§16. Chern Numbers and Pontrjagin Numbers --$t§17. The Oriented Cobordism Ring ?* --$t§18. Thom Spaces and Transversality --$t§19. Multiplicative Sequences and the Signature Theorem --$t§20. Combinatorial Pontrjagin Classes --$tEpilogue --$tAppendix A: Singular Homology and Cohomology --$tAppendix B: Bernoulli Numbers --$tAppendix C: Connections, Curvature, and Characteristic Classes --$tBibliography --$tIndex
330   $aThe theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds.In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers.Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
410  0$aAnnals of mathematics studies ;$vno. 76.
410  0$aPrinceton landmarks in mathematics and physics.
606   $aCharacteristic classes
610   $aAdditive group.
610   $aAxiom.
610   $aBasis (linear algebra).
610   $aBoundary (topology).
610   $aBundle map.
610   $aCW complex.
610   $aCanonical map.
610   $aCap product.
610   $aCartesian product.
610   $aCharacteristic class.
610   $aCharles Ehresmann.
610   $aChern class.
610   $aClassifying space.
610   $aCoefficient.
610   $aCohomology ring.
610   $aCohomology.
610   $aCompact space.
610   $aComplex dimension.
610   $aComplex manifold.
610   $aComplex vector bundle.
610   $aComplexification.
610   $aComputation.
610   $aConformal geometry.
610   $aContinuous function.
610   $aCoordinate space.
610   $aCross product.
610   $aDe Rham cohomology.
610   $aDiffeomorphism.
610   $aDifferentiable manifold.
610   $aDifferential form.
610   $aDifferential operator.
610   $aDimension (vector space).
610   $aDimension.
610   $aDirect sum.
610   $aDirectional derivative.
610   $aEilenberg?Steenrod axioms.
610   $aEmbedding.
610   $aEquivalence class.
610   $aEuler class.
610   $aEuler number.
610   $aExistence theorem.
610   $aExistential quantification.
610   $aExterior (topology).
610   $aFiber bundle.
610   $aFundamental class.
610   $aFundamental group.
610   $aGeneral linear group.
610   $aGrassmannian.
610   $aGysin sequence.
610   $aHausdorff space.
610   $aHomeomorphism.
610   $aHomology (mathematics).
610   $aHomotopy.
610   $aIdentity element.
610   $aInteger.
610   $aInterior (topology).
610   $aIsomorphism class.
610   $aJ-homomorphism.
610   $aK-theory.
610   $aLeibniz integral rule.
610   $aLevi-Civita connection.
610   $aLimit of a sequence.
610   $aLinear map.
610   $aMetric space.
610   $aNatural number.
610   $aNatural topology.
610   $aNeighbourhood (mathematics).
610   $aNormal bundle.
610   $aOpen set.
610   $aOrthogonal complement.
610   $aOrthogonal group.
610   $aOrthonormal basis.
610   $aPartition of unity.
610   $aPermutation.
610   $aPolynomial.
610   $aPower series.
610   $aPrincipal ideal domain.
610   $aProjection (mathematics).
610   $aRepresentation ring.
610   $aRiemannian manifold.
610   $aSequence.
610   $aSingular homology.
610   $aSmoothness.
610   $aSpecial case.
610   $aSteenrod algebra.
610   $aStiefel?Whitney class.
610   $aSubgroup.
610   $aSubset.
610   $aSymmetric function.
610   $aTangent bundle.
610   $aTensor product.
610   $aTheorem.
610   $aThom space.
610   $aTopological space.
610   $aTopology.
610   $aUnit disk.
610   $aUnit vector.
610   $aVariable (mathematics).
610   $aVector bundle.
610   $aVector space.
615  0$aCharacteristic classes.
676   $a514/.7
700   $aMilnor$b John$040532
702   $aStasheff$b James D.
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154754803321
996   $aCharacteristic Classes. (AM-76), Volume 76$92788043
997   $aUNINA