Topic
Frame bundle
About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: In this article, the pullback of a smooth principal fiber bundle over a paracompact manifold is defined, and it is shown that there is an isomorphism between pullbacks obtained from homotopy maps.
Abstract: We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article is to show that for a principal fibre bundle over a paracompact manifold, there is a principal fibre bundle isomorphism between pull-backs obtained from homotopic maps. This enables simple proofs of several results on the structure of principal fibre bundles. No new results are obtained---this is simply an accessible presentation of an important idea.
3 citations
TL;DR: In this paper, the authors show that the connection responsible for any Abelian or non-Abelian Aharonov-Bohm effect with n parallel magnetic flux lines in ℝ3 lies in a trivial G-principal bundle P→M, i.e. P is isomorphic to the product M×G, where G is any path connected topological group; in particular a connected Lie group.
Abstract: We show that the connection responsible for any Abelian or non-Abelian Aharonov–Bohm effect with n parallel “magnetic” flux lines in ℝ3, lies in a trivial G-principal bundle P→M, i.e. P is isomorphic to the product M×G, where G is any path connected topological group; in particular a connected Lie group. We also show that two other bundles are involved: the universal covering space \(\tilde{M}\to M\) , where path integrals are computed, and the associated bundle P× G ℂ m →M, where the wave function and its covariant derivative are sections.
3 citations
TL;DR: In this article, the authors consider line fields with n-and 2-dimensional smooth defect sets and study the relation between these two types of defect behavior, showing that the defect line fields can be classified into two classes: 1.
Abstract: Let E be an n-dimensional real vector bundle over an n-dimensional manifold M. A section in the projective bundle ℙE, defined everywhere except on a certain “defect set” Δ⊂M is called a defect line field in E. We consider line fields with n- and 2-codimensional smooth defect sets and study the relation between these two types of defect behavior. Details are given in [I].
3 citations
TL;DR: The equivalence class of bundle representations of a group G on the product bundle B0 with total space B0=X×Y includes all representations of G on bundles B which are homeomorphic (but not necessarily naturally homeomorphic) to the product X×Y, provided the G has the same action on the fibres of B0 and B.
Abstract: It is proved that the equivalence class of bundle representations of a group G on the product bundle B0 with total space B0=X×Y includes all representations of G on bundles B which are homeomorphic (but not necessarily naturally homeomorphic) to the product X×Y, provided the G has the same action on the fibres of B0 and B. The group A of the bundle B is immaterial.
3 citations
01 Oct 1965
TL;DR: In this paper, the idea of exact filling bundles is described roughly as follows: a vector bundle with fiber Rk, total space E(ξk) and base X, and a trivial n-plane bundle on X so that E(in) = X × Rn.
Abstract: The idea of exact filling bundle may be described roughly as follows. Suppose that ξk is a vector bundle with fibre Rk, total space E(ξk) and base X. We say that ξk is a real k-plane bundle on X. Let in be the trivial n-plane bundle on X so that E(in) = X × Rn. A bundle monomorphism j: ξk → in defines a map S0305004100039220_inline001: E(ξk)→Rn obtained by composition of the embedding E(ξk)→E(in) and the product projection E(in) → Rn. The map S0305004100039220_inline001 represents each fibre of ξk as a k-plane in Rn.
3 citations