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Frame bundle

About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.


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TL;DR: In this paper, the adjoint bundle associated with a G-bundle over M splits on mod p cohomology as an algebra, and it is shown that the isomorphism class of an SU(n)-adjoint bundle over M coincides with the homotopy equivalence class of the bundle.
Abstract: Let G be a nite loop space such that the mod p cohomology of the clas- sifying space BG is a polynomial algebra. We consider when the adjoint bundle associated with a G-bundle over M splits on mod p cohomology as an algebra. In the case p = 2, an obstruction for the adjoint bundle to admit such a splitting is found in the Hochschild homology concerning the mod 2 cohomologies of BG and M via a module derivation. Moreover the derivation tells us that the splitting is not compatible with the Steenrod operations in general. As a consequence, we can show that the isomorphism class of an SU(n)-adjoint bundle over a 4-dimensional CW complex coincides with the homotopy equivalence class of the bundle.

10 citations

Posted Content
TL;DR: In this article, a fiber bundle formulation of relativistic quantum mechanics is proposed, where wave functions are replaced with (state) sections or liftings of paths of a suitably chosen vector bundle over space-time whose (standard) fibre is the space of wave functions.
Abstract: We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in different directions. In the bundle description the wavefunctions are replaced with (state) sections (covariant approach) or liftings of paths (equivalently: sections along paths) (time-dependent approach) of a suitably chosen vector bundle over space-time whose (standard) fibre is the space of the wavefunctions. Now the quantum evolution is described as a linear transportation of the state sections/liftings in the (total) bundle space. The equations of these transportations turn to be the bundle versions of the corresponding relativistic wave equations. Connections between the (retarded) Green functions of these equations and the evolution operators and transports are found. Especially the Dirac and Klein-Gordon equations are considered.

10 citations

Posted Content
TL;DR: In this paper, a nonstandard (maximal) inclusion SO(3) in SO(5) associated with the irreducible representation \rho_5 of SO( 3) in R^5 is considered.
Abstract: A nonstandard (maximal) inclusion SO(3) in SO(5) associated with the irreducible representation \rho_5 of SO(3) in R^5 is considered. The topological obstructions for admitting the SO(3) structure on the frame bundle over 5-manifold are investigated. The necessary and sufficient conditions are formulated.

10 citations

Journal ArticleDOI
TL;DR: In this paper, new solutions to the Einstein-Cartan-Weyl system are presented and analyzed in the intrinsic language of complex quaternionic exterior forms, set up as a local gauge theory of the Lorentz group.
Abstract: New solutions to the Einstein-Cartan-Weyl system are presented and analysed in the intrinsic language of complex quaternionic exterior forms. The model is set up as a local gauge theory of the Lorentz group for critical sections of the linear frame bundle over space-time. Tentative suggestions are made for the interpretation of these solutions in the framework of a quantised interacting field system.

10 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202214
20214
202012
201911
201811