<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Tangent fibrations generate a “multi-floored tower”, while raising from one of its floors to the next one, one practically reiterates the previously performed actions. In this way, the "tower" admits a ladder-shaped structure. Raising to the first floors suffices for iteratively performing the subsequent steps. The paper mainly studies the tangent functor. We describe the structure of multiple vector bundle which naturally appears on the floors, tangent maps, sector-forms, the lift of vector fields to upper floors. Further, we show how tangent groups of Lie groups lead to gauge theory, and explain in this context the meaning of covariant differentiation. Finally, we will point out within the floors special subbundles - the osculating bundles, which play an essential role in classical theories. </p></abstract>

Tangent fibrations generate a “multi-floored tower”, while raising from one of its floors to the next one, one practically reiterates the previously performed actions. In this way, the "tower" admits a ladder-shaped structure. Raising to the first floors suffices for iteratively performing the subsequent steps. The paper mainly studies the tangent functor. We describe the structure of multiple vector bundle which naturally appears on the floors, tangent maps, sector-forms, the lift of vector fields to upper floors. Further, we show how tangent groups of Lie groups lead to gauge theory, and explain in this context the meaning of covariant differentiation. Finally, we will point out within the floors special subbundles - the osculating bundles, which play an essential role in classical theories.

Iterative calculus on tangent floors

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Iterative calculus on tangent floors"}

Tangent fibrations generate a “multi-floored tower”, while raising from one of its floors to the next one, one practically reiterates the previously performed...

Iterative calculus on tangent floors

Publié en ligne: 21 sept. 2017

Pages: 121 - 152

Reçu: 01 juil. 2014

Accepté: 28 juil. 2014

DOI: https://doi.org/10.1515/auom-2016-0007

Mots clés
tangent fibration, floor, tangent functor, lift, Lie groups, multiple vector bundle, covariant differentiation, gauge theory, osculating bundles

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Iterative calculus on tangent floors

Publié en ligne: 21 sept. 2017

Pages: 121 - 152

Reçu: 01 juil. 2014

Accepté: 28 juil. 2014

DOI: https://doi.org/10.1515/auom-2016-0007

Mots cléstangent fibration, floor, tangent functor, lift, Lie groups, multiple vector bundle, covariant differentiation, gauge theory, osculating bundles

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
tangent fibration, floor, tangent functor, lift, Lie groups, multiple vector bundle, covariant differentiation, gauge theory, osculating bundles