Structure of some mapping spaces

2025/04/15 by Liangzhao Zhang, Xiangyu Zhou, Zhang, Liangzhao +1
Mathematics · #Advanced Banach Space Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2504.11136

openalex publication_date 2025/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the path space of a differentiable manifold is diffeomorphic to a Fréchet space, endowing the path space with a linear structure. Furthermore, the base point preserving mapping space consisting of maps from a cube to a differentiable manifold is also diffeomorphic to a Fréchet space. As a corollary of a more general theorem, we prove that the path fibration becomes a fibre bundle for manifolds M. Additionally, we discuss the mapping space from a compact topological space to a differentiable manifold, demonstrating that this space admits the structure of a smooth Banach manifold.

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