ON THE GEOMETRY OF DIFFEOLOGICAL VECTOR PSEUDO-BUNDLES AND INFINITE DIMENSIONAL VECTOR BUNDLES: AUTOMORPHISMS, CONNECTIONS AND COVARIANT DERIVATIVES - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

ON THE GEOMETRY OF DIFFEOLOGICAL VECTOR PSEUDO-BUNDLES AND INFINITE DIMENSIONAL VECTOR BUNDLES: AUTOMORPHISMS, CONNECTIONS AND COVARIANT DERIVATIVES

Résumé

We consider here the category of diffeological vector pseudo-bundles, and study a possible extension of classical differential geometric tools on finite dimensional vector bundles, namely, the group of automorphisms, the frame bundle, the stace of connection 1-forms and the space of covariant drivatives. Substential distinctions are highlighted in this generalized framework, among which the non-isomorphism between connection 1-forms and covariant derivatives. Applications not only include finite dimensional examples wit singularities, but also infinite dimensional vector bundles whom base is not a smooth manifold with atlas, puching the definitions over the classical framework of infinite dimensional geometry.
Fichier principal
Vignette du fichier
VPB-automorphism.pdf (398.89 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03721730 , version 1 (12-07-2022)

Identifiants

  • HAL Id : hal-03721730 , version 1

Citer

Jean-Pierre Magnot. ON THE GEOMETRY OF DIFFEOLOGICAL VECTOR PSEUDO-BUNDLES AND INFINITE DIMENSIONAL VECTOR BUNDLES: AUTOMORPHISMS, CONNECTIONS AND COVARIANT DERIVATIVES. 2022. ⟨hal-03721730⟩
8 Consultations
52 Téléchargements

Partager

Gmail Facebook X LinkedIn More