Differentiable mappings between spaces of sections

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.

31 pages, LaTeX. Up to minor updates, this is an unpublished manuscript from 2001/2002

References in corpus (1)

• Lie groups over non-discrete topological fields

Cited by in corpus (4)

• Complexifications of infinite-dimensional manifolds and new constructions of infinite-dimensional Lie groups
• Universal continuous bilinear forms for compactly supported sections of Lie algebra bundles and universal continuous extensions of certain current algebras
• The Banach manifold $C^k(M,N)$
• Universal central extensions for groups of sections on non-compact manifolds