Structure of some mapping spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908320517849088 |
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| author | Zhang, Liangzhao Zhou, Xiangyu |
| author_facet | Zhang, Liangzhao Zhou, Xiangyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure of some mapping spaces Zhang, Liangzhao Zhou, Xiangyu Differential Geometry 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. |
| title | Structure of some mapping spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.11136 |