Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Vector_bundle> ?p ?o }
- Vector_bundle abstract "In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g. a topological space, manifold, or algebraic variety), which is then called a vector bundle over X.The simplest example is the case that the family of vector spaces is constant, i.e., there is a fixed vector space V such that V(x) = V for all x in X: in this case there is a copy of V for each x in X and these copies fit together to form the vector bundle X × V over X. Such vector bundles are said to be trivial. A more complicated (and prototypical) class of examples are the tangent bundles of smooth (or differentiable) manifolds: to every point of such a manifold we attach the tangent space to the manifold at that point. Tangent bundles are not, in general, trivial bundles: for example, the tangent bundle of the sphere is non-trivial by the hairy ball theorem. In general, a manifold is said to be parallelizable if and only if its tangent bundle is trivial.Vector bundles are almost always required to be locally trivial, however, which means they are examples of fiber bundles. Also, the vector spaces are usually required to be over the real or complex numbers, in which case the vector bundle is said to be a real or complex vector bundle (respectively). Complex vector bundles can be viewed as real vector bundles with additional structure. In the following, we focus on real vector bundles in the category of topological spaces.".
- Vector_bundle thumbnail Mobius_strip_illus.svg?width=300.
- Vector_bundle wikiPageExternalLink VBpage.html.
- Vector_bundle wikiPageExternalLink smooth.html.
- Vector_bundle wikiPageExternalLink why-is-it-useful-to-classify-the-vector-bundles-of-a-space.
- Vector_bundle wikiPageExternalLink why-is-it-useful-to-study-vector-bundles.
- Vector_bundle wikiPageID "276524".
- Vector_bundle wikiPageLength "24145".
- Vector_bundle wikiPageOutDegree "109".
- Vector_bundle wikiPageRevisionID "680625899".
- Vector_bundle wikiPageWikiLink Abelian_category.
- Vector_bundle wikiPageWikiLink Algebraic_geometry.
- Vector_bundle wikiPageWikiLink Algebraic_variety.
- Vector_bundle wikiPageWikiLink Algebraic_vector_bundle.
- Vector_bundle wikiPageWikiLink Analytic_function.
- Vector_bundle wikiPageWikiLink Banach_bundle.
- Vector_bundle wikiPageWikiLink Banach_manifold.
- Vector_bundle wikiPageWikiLink Banach_space.
- Vector_bundle wikiPageWikiLink Bott_periodicity.
- Vector_bundle wikiPageWikiLink Bott_periodicity_theorem.
- Vector_bundle wikiPageWikiLink Bundle_map.
- Vector_bundle wikiPageWikiLink Cartesian_product.
- Vector_bundle wikiPageWikiLink Category:Vector_bundles.
- Vector_bundle wikiPageWikiLink Category_(mathematics).
- Vector_bundle wikiPageWikiLink Category_of_topological_spaces.
- Vector_bundle wikiPageWikiLink Category_theory.
- Vector_bundle wikiPageWikiLink Characteristic_class.
- Vector_bundle wikiPageWikiLink Classifying_space.
- Vector_bundle wikiPageWikiLink Coherent_sheaf.
- Vector_bundle wikiPageWikiLink Commutative_diagram.
- Vector_bundle wikiPageWikiLink Compact_support.
- Vector_bundle wikiPageWikiLink Complex_vector_bundle.
- Vector_bundle wikiPageWikiLink Connection_(vector_bundle).
- Vector_bundle wikiPageWikiLink Continuous_function.
- Vector_bundle wikiPageWikiLink Continuously_differentiable.
- Vector_bundle wikiPageWikiLink Definite_bilinear_form.
- Vector_bundle wikiPageWikiLink Definite_quadratic_form.
- Vector_bundle wikiPageWikiLink Diffeomorphism.
- Vector_bundle wikiPageWikiLink Differentiable_function.
- Vector_bundle wikiPageWikiLink Dimension_(vector_space).
- Vector_bundle wikiPageWikiLink Direct_sum_of_modules.
- Vector_bundle wikiPageWikiLink Dual_bundle.
- Vector_bundle wikiPageWikiLink Dual_space.
- Vector_bundle wikiPageWikiLink Dual_vector_space.
- Vector_bundle wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Vector_bundle wikiPageWikiLink Eigenvector.
- Vector_bundle wikiPageWikiLink Exact_sequence.
- Vector_bundle wikiPageWikiLink Fiber_bundle.
- Vector_bundle wikiPageWikiLink Function_(mathematics).
- Vector_bundle wikiPageWikiLink Functor.
- Vector_bundle wikiPageWikiLink Functorial.
- Vector_bundle wikiPageWikiLink Graduate_Studies_in_Mathematics.
- Vector_bundle wikiPageWikiLink Grassmannian.
- Vector_bundle wikiPageWikiLink Hairy_ball_theorem.
- Vector_bundle wikiPageWikiLink Hamel_dimension.
- Vector_bundle wikiPageWikiLink Hassler_Whitney.
- Vector_bundle wikiPageWikiLink Holomorphic_vector_bundle.
- Vector_bundle wikiPageWikiLink Homeomorphism.
- Vector_bundle wikiPageWikiLink Identity_function.
- Vector_bundle wikiPageWikiLink Infinitely_differentiable.
- Vector_bundle wikiPageWikiLink KO-theory.
- Vector_bundle wikiPageWikiLink Kernel_(category_theory).
- Vector_bundle wikiPageWikiLink Line_bundle.
- Vector_bundle wikiPageWikiLink Linear_complex_structure.
- Vector_bundle wikiPageWikiLink Linear_map.
- Vector_bundle wikiPageWikiLink Locally_connected_space.
- Vector_bundle wikiPageWikiLink Locally_constant.
- Vector_bundle wikiPageWikiLink Locally_constant_function.
- Vector_bundle wikiPageWikiLink Locally_free_sheaf.
- Vector_bundle wikiPageWikiLink Manifold.
- Vector_bundle wikiPageWikiLink MathOverflow.
- Vector_bundle wikiPageWikiLink Mathematics.
- Vector_bundle wikiPageWikiLink Metric_(vector_bundle).
- Vector_bundle wikiPageWikiLink Module_(mathematics).
- Vector_bundle wikiPageWikiLink Morphism.
- Vector_bundle wikiPageWikiLink Natural_number.
- Vector_bundle wikiPageWikiLink Parallelizable_manifold.
- Vector_bundle wikiPageWikiLink Picard_group.
- Vector_bundle wikiPageWikiLink Projective_space.
- Vector_bundle wikiPageWikiLink Pullback_bundle.
- Vector_bundle wikiPageWikiLink Raoul_Bott.
- Vector_bundle wikiPageWikiLink Real_analytic.
- Vector_bundle wikiPageWikiLink Real_number.
- Vector_bundle wikiPageWikiLink Reduction_of_the_structure_group.
- Vector_bundle wikiPageWikiLink Reduction_of_the_structure_group_of_a_bundle.
- Vector_bundle wikiPageWikiLink Scheme_(mathematics).
- Vector_bundle wikiPageWikiLink Secondary_vector_bundle_structure.
- Vector_bundle wikiPageWikiLink Section_(fiber_bundle).
- Vector_bundle wikiPageWikiLink Sheaf_(mathematics).
- Vector_bundle wikiPageWikiLink Sheaf_of_modules.
- Vector_bundle wikiPageWikiLink Smooth_functor.
- Vector_bundle wikiPageWikiLink Smooth_morphism.
- Vector_bundle wikiPageWikiLink Smoothness.
- Vector_bundle wikiPageWikiLink Sphere_bundle.
- Vector_bundle wikiPageWikiLink Splitting_principle.
- Vector_bundle wikiPageWikiLink Springer-Verlag.
- Vector_bundle wikiPageWikiLink Springer_Science+Business_Media.
- Vector_bundle wikiPageWikiLink Stable_bundle.
- Vector_bundle wikiPageWikiLink Stable_vector_bundle.
- Vector_bundle wikiPageWikiLink Support_(mathematics).