Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Principal_bundle> ?p ?o }
- Principal_bundle abstract "In mathematics, a principal bundle is a mathematical object which formalizes some of the essential features of the Cartesian product X × G of a space X with a group G. In the same way as with the Cartesian product, a principal bundle P is equipped with An action of G on P, analogous to (x, g)h = (x, gh) for a product space. A projection onto X. For a product space, this is just the projection onto the first factor, (x,g) ↦ x.Unlike a product space, principal bundles lack a preferred choice of identity cross-section; they have no preferred analog of (x,e). Likewise, there is not generally a projection onto G generalizing the projection onto the second factor, X × G → G which exists for the Cartesian product. They may also have a complicated topology, which prevents them from being realized as a product space even if a number of arbitrary choices are made to try to define such a structure by defining it on smaller pieces of the space.A common example of a principal bundle is the frame bundle FE of a vector bundle E, which consists of all ordered bases of the vector space attached to each point. The group G in this case is the general linear group, which acts on the right in the usual way: by changes of basis. Since there is no preferred way to choose an ordered basis of a vector space, a frame bundle lacks a canonical choice of identity cross-section.Principal bundles have important applications in topology and differential geometry. They have also found application in physics where they form part of the foundational framework of gauge theories. Principal bundles provide a unifying framework for the theory of fiber bundles in the sense that all fiber bundles with structure group G determine a unique principal G-bundle from which the original bundle can be reconstructed.".
- Principal_bundle wikiPageID "310950".
- Principal_bundle wikiPageLength "17942".
- Principal_bundle wikiPageOutDegree "95".
- Principal_bundle wikiPageRevisionID "697698601".
- Principal_bundle wikiPageWikiLink Almost_complex_manifold.
- Principal_bundle wikiPageWikiLink Associated_bundle.
- Principal_bundle wikiPageWikiLink Atlas_(topology).
- Principal_bundle wikiPageWikiLink Basis_(linear_algebra).
- Principal_bundle wikiPageWikiLink Bijection.
- Principal_bundle wikiPageWikiLink Cartesian_product.
- Principal_bundle wikiPageWikiLink Category:Differential_geometry.
- Principal_bundle wikiPageWikiLink Category:Fiber_bundles.
- Principal_bundle wikiPageWikiLink Category:Group_actions.
- Principal_bundle wikiPageWikiLink Category_(mathematics).
- Principal_bundle wikiPageWikiLink Change_of_basis.
- Principal_bundle wikiPageWikiLink Circle_group.
- Principal_bundle wikiPageWikiLink Complex_projective_space.
- Principal_bundle wikiPageWikiLink Connection_(principal_bundle).
- Principal_bundle wikiPageWikiLink Continuous_function.
- Principal_bundle wikiPageWikiLink Covering_space.
- Principal_bundle wikiPageWikiLink Diffeomorphism.
- Principal_bundle wikiPageWikiLink Differentiable_manifold.
- Principal_bundle wikiPageWikiLink Differential_geometry.
- Principal_bundle wikiPageWikiLink Equivariant_map.
- Principal_bundle wikiPageWikiLink Faithful_representation.
- Principal_bundle wikiPageWikiLink Fiber_bundle.
- Principal_bundle wikiPageWikiLink Frame_bundle.
- Principal_bundle wikiPageWikiLink G-fibration.
- Principal_bundle wikiPageWikiLink G-structure.
- Principal_bundle wikiPageWikiLink Gauge_theory.
- Principal_bundle wikiPageWikiLink General_linear_group.
- Principal_bundle wikiPageWikiLink Group_(mathematics).
- Principal_bundle wikiPageWikiLink Group_action.
- Principal_bundle wikiPageWikiLink Hausdorff_space.
- Principal_bundle wikiPageWikiLink Homeomorphism.
- Principal_bundle wikiPageWikiLink Homogeneous_space.
- Principal_bundle wikiPageWikiLink Homotopy_group.
- Principal_bundle wikiPageWikiLink Hopf_fibration.
- Principal_bundle wikiPageWikiLink Identity_element.
- Principal_bundle wikiPageWikiLink Lie_group.
- Principal_bundle wikiPageWikiLink Mathematics.
- Principal_bundle wikiPageWikiLink Metric_tensor.
- Principal_bundle wikiPageWikiLink Möbius_strip.
- Principal_bundle wikiPageWikiLink Normal_subgroup.
- Principal_bundle wikiPageWikiLink Open_set.
- Principal_bundle wikiPageWikiLink Orientability.
- Principal_bundle wikiPageWikiLink Orthogonal_group.
- Principal_bundle wikiPageWikiLink Orthonormality.
- Principal_bundle wikiPageWikiLink Paracompact_space.
- Principal_bundle wikiPageWikiLink Parallelizable_manifold.
- Principal_bundle wikiPageWikiLink Physics.
- Principal_bundle wikiPageWikiLink Principal_homogeneous_space.
- Principal_bundle wikiPageWikiLink Product_topology.
- Principal_bundle wikiPageWikiLink Projective_space.
- Principal_bundle wikiPageWikiLink Proper_map.
- Principal_bundle wikiPageWikiLink Pullback_bundle.
- Principal_bundle wikiPageWikiLink Quaternionic_projective_space.
- Principal_bundle wikiPageWikiLink Real_projective_space.
- Principal_bundle wikiPageWikiLink Reduction_of_the_structure_group.
- Principal_bundle wikiPageWikiLink Representation_theory.
- Principal_bundle wikiPageWikiLink Riemannian_manifold.
- Principal_bundle wikiPageWikiLink Section_(fiber_bundle).
- Principal_bundle wikiPageWikiLink Smoothness.
- Principal_bundle wikiPageWikiLink Sphere.
- Principal_bundle wikiPageWikiLink Spin_group.
- Principal_bundle wikiPageWikiLink Spin_structure.
- Principal_bundle wikiPageWikiLink Submersion_(mathematics).
- Principal_bundle wikiPageWikiLink Symplectic_group.
- Principal_bundle wikiPageWikiLink Tangent_space.
- Principal_bundle wikiPageWikiLink Topological_group.
- Principal_bundle wikiPageWikiLink Topology.
- Principal_bundle wikiPageWikiLink Vector_bundle.
- Principal_bundle wikiPageWikiLink Weakly_contractible.
- Principal_bundle wikiPageWikiLinkText "Principal bundle".
- Principal_bundle wikiPageWikiLinkText "bundle of principal connections".
- Principal_bundle wikiPageWikiLinkText "bundle".
- Principal_bundle wikiPageWikiLinkText "connection forms".
- Principal_bundle wikiPageWikiLinkText "gauge bundle".
- Principal_bundle wikiPageWikiLinkText "principal ''G''-bundle".
- Principal_bundle wikiPageWikiLinkText "principal ''G''-bundles".
- Principal_bundle wikiPageWikiLinkText "principal ''H''-bundle".
- Principal_bundle wikiPageWikiLinkText "principal ''K''-bundle".
- Principal_bundle wikiPageWikiLinkText "principal ''N''-bundle".
- Principal_bundle wikiPageWikiLinkText "principal ''U''(1)-bundle".
- Principal_bundle wikiPageWikiLinkText "principal ''U''(1)-bundles".
- Principal_bundle wikiPageWikiLinkText "principal -bundle".
- Principal_bundle wikiPageWikiLinkText "principal G-bundle".
- Principal_bundle wikiPageWikiLinkText "principal GL(''n'')-bundle".
- Principal_bundle wikiPageWikiLinkText "principal Sp(1)-bundle".
- Principal_bundle wikiPageWikiLinkText "principal U(''n'')-bundle".
- Principal_bundle wikiPageWikiLinkText "principal U(1)-bundle".
- Principal_bundle wikiPageWikiLinkText "principal bundle".
- Principal_bundle wikiPageWikiLinkText "principal bundles".
- Principal_bundle wikiPageWikiLinkText "principal".
- Principal_bundle wikiPageWikiLinkText "reduction".
- Principal_bundle wikiPageWikiLinkText "structure group".
- Principal_bundle wikiPageUsesTemplate Template:=.
- Principal_bundle wikiPageUsesTemplate Template:Cite_book.
- Principal_bundle wikiPageUsesTemplate Template:Main.