On the geometry of diffeological vector pseudo-bundles and infinite dimensional vector bundles: automorphisms, connections and covariant derivatives
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Publication:6507904
arXiv2207.06824MaRDI QIDQ6507904
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Abstract: 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.
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