Functorial construction of functional spaces on vector bundles

26.11.2020, 16:15  –  Online-Seminar
Forschungsseminar Differentialgeometrie

Rubens Longhi (UP)

A suitable category of vector bundles will be introduced, in which every object is obtained as a limit of trivial vector bundles. Then, a functorial definition for general functional spaces will be provided for sections of a vector bundle. Spaces of locally defined sections will behave contravariantly, while spaces of compactly supported ones will behave covariantly. This will allow to extract information about the general features of a functional space just by looking at the corresponding functional space on a ball of \(\mathbb{R}^n\).

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