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- Stiefel–Whitney_class abstract "In mathematics, in particular in algebraic topology and differential geometry, the Stiefel–Whitney classes are a set of topological invariants of a real vector bundle that describe the obstructions to constructing everywhere independent sets of sections of the vector bundle. Stiefel–Whitney classes are indexed from 0 to n, where n is the dimension of the vector space fiber of the vector bundle. If the Stiefel–Whitney class of index i is nonzero, then there cannot exist (n−i+1) everywhere linearly independent sections of the vector bundle. A nonzero nth Stiefel–Whitney class indicates that every section of the bundle must vanish at some point. A nonzero first Stiefel–Whitney class indicates that the vector bundle is not orientable. For example, the first Stiefel–Whitney class of the Möbius strip, as a line bundle over the circle, is not zero, whereas the first Stiefel–Whitney class of the trivial line bundle over the circle, S1×R is zero.The Stiefel–Whitney class was named for Eduard Stiefel and Hassler Whitney and is an example of a Z/2Z-characteristic class associated to real vector bundles.In algebraic geometry one can also define analogous Stiefel–Whitney classes for vector bundles with a non-degenerate quadratic form, taking values in etale cohomology groups or in Milnor K-theory. As a special case one can define Stiefel–Whitney classes for quadratic forms over fields, the first two cases being the discriminant and the Hasse–Witt invariant (Milnor 1970).".
- Stiefel–Whitney_class wikiPageExternalLink ConciseRevised.pdf.
- Stiefel–Whitney_class wikiPageExternalLink External_links.
- Stiefel–Whitney_class wikiPageID "877761".
- Stiefel–Whitney_class wikiPageLength "22489".
- Stiefel–Whitney_class wikiPageOutDegree "102".
- Stiefel–Whitney_class wikiPageRevisionID "675979332".
- Stiefel–Whitney_class wikiPageWikiLink Algebraic_topology.
- Stiefel–Whitney_class wikiPageWikiLink Antipodal_point.
- Stiefel–Whitney_class wikiPageWikiLink Antipodal_points.
- Stiefel–Whitney_class wikiPageWikiLink Bijection.
- Stiefel–Whitney_class wikiPageWikiLink Bockstein_homomorphism.
- Stiefel–Whitney_class wikiPageWikiLink CW-complex.
- Stiefel–Whitney_class wikiPageWikiLink CW_complex.
- Stiefel–Whitney_class wikiPageWikiLink Canonical_form.
- Stiefel–Whitney_class wikiPageWikiLink Category:Characteristic_classes.
- Stiefel–Whitney_class wikiPageWikiLink Characteristic_class.
- Stiefel–Whitney_class wikiPageWikiLink Chern_class.
- Stiefel–Whitney_class wikiPageWikiLink Classifying_space.
- Stiefel–Whitney_class wikiPageWikiLink Cobordism.
- Stiefel–Whitney_class wikiPageWikiLink Cohomology.
- Stiefel–Whitney_class wikiPageWikiLink Cohomology_group.
- Stiefel–Whitney_class wikiPageWikiLink Cohomology_ring.
- Stiefel–Whitney_class wikiPageWikiLink Commutative_ring.
- Stiefel–Whitney_class wikiPageWikiLink Complex_vector_bundle.
- Stiefel–Whitney_class wikiPageWikiLink Continuous_function.
- Stiefel–Whitney_class wikiPageWikiLink Contractible.
- Stiefel–Whitney_class wikiPageWikiLink Contractible_space.
- Stiefel–Whitney_class wikiPageWikiLink Cup_product.
- Stiefel–Whitney_class wikiPageWikiLink Cyclic_group.
- Stiefel–Whitney_class wikiPageWikiLink De_Rham_invariant.
- Stiefel–Whitney_class wikiPageWikiLink Differential_geometry.
- Stiefel–Whitney_class wikiPageWikiLink Direct_sum_of_modules.
- Stiefel–Whitney_class wikiPageWikiLink Eduard_Stiefel.
- Stiefel–Whitney_class wikiPageWikiLink Eilenberg-Maclane_space.
- Stiefel–Whitney_class wikiPageWikiLink Eilenberg–MacLane_space.
- Stiefel–Whitney_class wikiPageWikiLink Euler_characteristic.
- Stiefel–Whitney_class wikiPageWikiLink Euler_class.
- Stiefel–Whitney_class wikiPageWikiLink Fiber_(mathematics).
- Stiefel–Whitney_class wikiPageWikiLink Fiber_bundle.
- Stiefel–Whitney_class wikiPageWikiLink Fundamental_class.
- Stiefel–Whitney_class wikiPageWikiLink Grassmannian.
- Stiefel–Whitney_class wikiPageWikiLink Group_(mathematics).
- Stiefel–Whitney_class wikiPageWikiLink Hasse_invariant_of_a_quadratic_form.
- Stiefel–Whitney_class wikiPageWikiLink Hasse–Witt_invariant.
- Stiefel–Whitney_class wikiPageWikiLink Hassler_Whitney.
- Stiefel–Whitney_class wikiPageWikiLink Homology_manifold.
- Stiefel–Whitney_class wikiPageWikiLink Homotopy_group.
- Stiefel–Whitney_class wikiPageWikiLink Integer_partition.
- Stiefel–Whitney_class wikiPageWikiLink Invariant_(mathematics).
- Stiefel–Whitney_class wikiPageWikiLink Inventiones_Mathematicae.
- Stiefel–Whitney_class wikiPageWikiLink Isomorphic.
- Stiefel–Whitney_class wikiPageWikiLink Isomorphism.
- Stiefel–Whitney_class wikiPageWikiLink Jacobian_variety.
- Stiefel–Whitney_class wikiPageWikiLink Lev_Pontryagin.
- Stiefel–Whitney_class wikiPageWikiLink Line_bundle.
- Stiefel–Whitney_class wikiPageWikiLink Linear_independence.
- Stiefel–Whitney_class wikiPageWikiLink Linearly_independent.
- Stiefel–Whitney_class wikiPageWikiLink Mathematics.
- Stiefel–Whitney_class wikiPageWikiLink Milnor_K-theory.
- Stiefel–Whitney_class wikiPageWikiLink Modular_arithmetic.
- Stiefel–Whitney_class wikiPageWikiLink Möbius_strip.
- Stiefel–Whitney_class wikiPageWikiLink N-sphere.
- Stiefel–Whitney_class wikiPageWikiLink Obstruction_theory.
- Stiefel–Whitney_class wikiPageWikiLink Orientability.
- Stiefel–Whitney_class wikiPageWikiLink Orientable.
- Stiefel–Whitney_class wikiPageWikiLink Paracompact_space.
- Stiefel–Whitney_class wikiPageWikiLink Partition_(number_theory).
- Stiefel–Whitney_class wikiPageWikiLink Projective_space.
- Stiefel–Whitney_class wikiPageWikiLink Pullback_bundle.
- Stiefel–Whitney_class wikiPageWikiLink Real_projective_space.
- Stiefel–Whitney_class wikiPageWikiLink René_Thom.
- Stiefel–Whitney_class wikiPageWikiLink Section_(fiber_bundle).
- Stiefel–Whitney_class wikiPageWikiLink Singular_cohomology.
- Stiefel–Whitney_class wikiPageWikiLink Singular_homology.
- Stiefel–Whitney_class wikiPageWikiLink Sphere.
- Stiefel–Whitney_class wikiPageWikiLink Spin_structure.
- Stiefel–Whitney_class wikiPageWikiLink Splitting_principle.
- Stiefel–Whitney_class wikiPageWikiLink Steenrod_algebra.
- Stiefel–Whitney_class wikiPageWikiLink Steenrod_square.
- Stiefel–Whitney_class wikiPageWikiLink Stiefel_manifold.
- Stiefel–Whitney_class wikiPageWikiLink Surgery_theory.
- Stiefel–Whitney_class wikiPageWikiLink Tangent_bundle.
- Stiefel–Whitney_class wikiPageWikiLink Tautological_bundle.
- Stiefel–Whitney_class wikiPageWikiLink Tautological_line_bundle.
- Stiefel–Whitney_class wikiPageWikiLink Topological_invariant.
- Stiefel–Whitney_class wikiPageWikiLink Topological_property.
- Stiefel–Whitney_class wikiPageWikiLink Topological_space.
- Stiefel–Whitney_class wikiPageWikiLink Topological_spaces.
- Stiefel–Whitney_class wikiPageWikiLink Trivial_bundle.
- Stiefel–Whitney_class wikiPageWikiLink Vector_bundle.
- Stiefel–Whitney_class wikiPageWikiLink Whitney_sum.
- Stiefel–Whitney_class wikiPageWikiLink Wu_Wenjun.
- Stiefel–Whitney_class wikiPageWikiLink Étale_cohomology.
- Stiefel–Whitney_class wikiPageWikiLinkText "Stiefel%E2%80%93Whitney_class#Stiefel.E2.80.93Whitney_numbers".
- Stiefel–Whitney_class wikiPageWikiLinkText "Stiefel–Whitney characteristic class".
- Stiefel–Whitney_class wikiPageWikiLinkText "Stiefel–Whitney class".
- Stiefel–Whitney_class wikiPageWikiLinkText "Stiefel–Whitney class#Stiefel.E2.80.93Whitney_numbers".
- Stiefel–Whitney_class wikiPageWikiLinkText "Stiefel–Whitney class#Wu classes".
- Stiefel–Whitney_class wikiPageWikiLinkText "Stiefel–Whitney class#Wu formula".