Differentiable mappings between spaces of sections

2013/08/06 by Helge Glöckner, Helge Glockner, Glockner, Helge · 2 citations
Mathematics · #22E67 (primary) 46E25 #46T20 #58C25 (secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #math.FA #msc:22E67 #msc:46E25 #msc:46T20 #msc:58C25

paper · pdf · doi:10.48550/arxiv.1308.1172

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 Up to minor updates, this is an unpublished manuscript from 2001/2002

arxiv created 2013/08/06 · openalex publication_date 2013/08/06 · arxiv updated 2013/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• The Banach manifold C^k(M,N)
• Universal central extensions for groups of sections on non-compact manifolds

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