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arXiv · 1308.1172

Differentiable mappings between spaces of sections

Helge Glockner
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Abstract

In this work, various versions of the so-called Omega-Lemma are provided, which ensure differentiability properties of pushforwrds between spaces of C^r-sections (or compactly supported C^r-sections) in vector bundles over finite-dimensional base manifolds whose fibres are (possibly infinite-dimensional) locally convex spaces. Applications are given, including the proof of continuity for some natural module multiplications on spaces of sections and the construction of certain infinite-dimensional Lie groups of Lie group-valued maps.

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Helge Glockner. 2013-08-06. Differentiable mappings between spaces of sections. https://arxiv.org/abs/1308.1172

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