The Banach manifold C^k(M,N)

2018/02/21 by Johannes Wittmann, Wittmann, Johannes
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1802.07548

openalex publication_date 2018/02/21 · arxiv created 2019/01/30 · arxiv updated 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a closed manifold and let N be a connected manifold without boundary. For each k∈ℕ the set of k times continuously differentiable maps between M and N has the structure of a smooth Banach manifold where the underlying manifold topology is the compact-open C^k topology. We provide a detailed and rigorous proof for this important statement which is already partially covered by existing literature.

Citations

• Differentiable mappings between spaces of sections

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