Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Line_bundle> ?p ?o }
Showing triples 1 to 100 of
100
with 100 triples per page.
- Line_bundle abstract "In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising these. More formally, in algebraic topology and differential topology a line bundle is defined as a vector bundle of rank 1.Line bundles are specified by choosing a one-dimensional vector space for each point of the space in a continuous manner. In topological applications, this vector space is usually real or complex. The two cases display fundamentally different behavior because of the different topological properties of real and complex vector spaces: If the origin is removed from the real line, then the result is the set of 1×1 invertible real matrices, which is homotopy-equivalent to a discrete two-point space by contracting the positive and negative reals each to a point; whereas removing the origin from the complex plane yields the 1×1 invertible complex matrices, which have the homotopy type of a circle.From the perspective of homotopy theory, a real line bundle therefore behaves much the same as a fiber bundle with a two-point fiber, that is, like a double cover. A special case of this is the orientable double cover of a differentiable manifold, where the corresponding line bundle is the determinant bundle of the tangent bundle (see below). The Möbius strip corresponds to a double cover of the circle (the θ → 2θ mapping) and by changing the fiber, can also be viewed as having a two-point fiber, the unit interval as a fiber, or the real line.Complex line bundles are closely related to circle bundles. There are some celebrated ones, for example the Hopf fibrations of spheres to spheres.In algebraic geometry, an invertible sheaf (i.e., locally free sheaf of rank one) is often called a line bundle.".
- Line_bundle wikiPageExternalLink line_bundles.pdf.
- Line_bundle wikiPageID "361366".
- Line_bundle wikiPageLength "11013".
- Line_bundle wikiPageOutDegree "63".
- Line_bundle wikiPageRevisionID "674543312".
- Line_bundle wikiPageWikiLink Algebraic_geometry.
- Line_bundle wikiPageWikiLink Algebraic_topology.
- Line_bundle wikiPageWikiLink CW_complex.
- Line_bundle wikiPageWikiLink Category:Algebraic_topology.
- Line_bundle wikiPageWikiLink Category:Differential_topology.
- Line_bundle wikiPageWikiLink Category:Homotopy_theory.
- Line_bundle wikiPageWikiLink Category:Vector_bundles.
- Line_bundle wikiPageWikiLink Characteristic_class.
- Line_bundle wikiPageWikiLink Chern_class.
- Line_bundle wikiPageWikiLink Circle_bundle.
- Line_bundle wikiPageWikiLink Classifying_space.
- Line_bundle wikiPageWikiLink Coherent_sheaf.
- Line_bundle wikiPageWikiLink Complex_manifold.
- Line_bundle wikiPageWikiLink Contractible.
- Line_bundle wikiPageWikiLink Contractible_space.
- Line_bundle wikiPageWikiLink Cotangent_bundle.
- Line_bundle wikiPageWikiLink Covering_space.
- Line_bundle wikiPageWikiLink Differentiable_manifold.
- Line_bundle wikiPageWikiLink Differential_topology.
- Line_bundle wikiPageWikiLink Discrete_two-point_space.
- Line_bundle wikiPageWikiLink Double_cover_(topology).
- Line_bundle wikiPageWikiLink Exponential_sequence.
- Line_bundle wikiPageWikiLink Exponential_sheaf_sequence.
- Line_bundle wikiPageWikiLink Exterior_algebra.
- Line_bundle wikiPageWikiLink Exterior_power.
- Line_bundle wikiPageWikiLink Fiber_bundle.
- Line_bundle wikiPageWikiLink Finitely_generated_module.
- Line_bundle wikiPageWikiLink Group_action.
- Line_bundle wikiPageWikiLink Holomorphic_line_bundle.
- Line_bundle wikiPageWikiLink Holomorphic_vector_bundle.
- Line_bundle wikiPageWikiLink Homogeneous_coordinates.
- Line_bundle wikiPageWikiLink Homotopy.
- Line_bundle wikiPageWikiLink Homotopy_theory.
- Line_bundle wikiPageWikiLink Hopf_fibration.
- Line_bundle wikiPageWikiLink I-bundle.
- Line_bundle wikiPageWikiLink Inverse_element.
- Line_bundle wikiPageWikiLink Invertible.
- Line_bundle wikiPageWikiLink Invertible_sheaf.
- Line_bundle wikiPageWikiLink Kodaira_embedding_theorem.
- Line_bundle wikiPageWikiLink Lefschetz_pencil.
- Line_bundle wikiPageWikiLink Locally_free_sheaf.
- Line_bundle wikiPageWikiLink Mathematics.
- Line_bundle wikiPageWikiLink Möbius_strip.
- Line_bundle wikiPageWikiLink Orientability.
- Line_bundle wikiPageWikiLink Orientable_double_cover.
- Line_bundle wikiPageWikiLink Orientable_manifold.
- Line_bundle wikiPageWikiLink Pontryagin_class.
- Line_bundle wikiPageWikiLink Principal_bundle.
- Line_bundle wikiPageWikiLink Projective_module.
- Line_bundle wikiPageWikiLink Projective_space.
- Line_bundle wikiPageWikiLink Quaternion.
- Line_bundle wikiPageWikiLink Robin_Hartshorne.
- Line_bundle wikiPageWikiLink Sheaf_(mathematics).
- Line_bundle wikiPageWikiLink Smooth_manifold.
- Line_bundle wikiPageWikiLink Smooth_structure.
- Line_bundle wikiPageWikiLink Sphere.
- Line_bundle wikiPageWikiLink Splitting_principle.
- Line_bundle wikiPageWikiLink Stiefel-Whitney_class.
- Line_bundle wikiPageWikiLink Stiefel–Whitney_class.
- Line_bundle wikiPageWikiLink Tangent.
- Line_bundle wikiPageWikiLink Tangent_bundle.
- Line_bundle wikiPageWikiLink Tensor_density.
- Line_bundle wikiPageWikiLink Tensor_product.
- Line_bundle wikiPageWikiLink Unit_interval.
- Line_bundle wikiPageWikiLink Universal_property.
- Line_bundle wikiPageWikiLink Vector_bundle.
- Line_bundle wikiPageWikiLinkText "Line bundle".
- Line_bundle wikiPageWikiLinkText "line bundle".
- Line_bundle wikiPageWikiLinkText "line bundle#Determinant bundles".
- Line_bundle hasPhotoCollection Line_bundle.
- Line_bundle wikiPageUsesTemplate Template:Main.
- Line_bundle wikiPageUsesTemplate Template:Mergefrom.
- Line_bundle wikiPageUsesTemplate Template:Nowrap_end.
- Line_bundle wikiPageUsesTemplate Template:Reflist.
- Line_bundle subject Category:Algebraic_topology.
- Line_bundle subject Category:Differential_topology.
- Line_bundle subject Category:Homotopy_theory.
- Line_bundle subject Category:Vector_bundles.
- Line_bundle type Article.
- Line_bundle type Article.
- Line_bundle type Bundle.
- Line_bundle type Mapping.
- Line_bundle type Physic.
- Line_bundle comment "In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising these. More formally, in algebraic topology and differential topology a line bundle is defined as a vector bundle of rank 1.Line bundles are specified by choosing a one-dimensional vector space for each point of the space in a continuous manner.".
- Line_bundle label "Line bundle".
- Line_bundle sameAs Geradenbündel.
- Line_bundle sameAs 直線束.
- Line_bundle sameAs 선다발.
- Line_bundle sameAs Fibrado_de_linhas.
- Line_bundle sameAs m.01_h4v.
- Line_bundle sameAs Q1509762.
- Line_bundle sameAs Q1509762.
- Line_bundle wasDerivedFrom Line_bundle?oldid=674543312.
- Line_bundle isPrimaryTopicOf Line_bundle.