On the isotopy classes of embeddings of surfaces in 5-manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918379520000000 |
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| author | Qiao, Ruoyu |
| author_facet | Qiao, Ruoyu |
| contents | Let f, g be two homotopic smooth embeddings of a closed surface in a closed oriented 5-dimensional manifold. We show that if f admits a common algebraic dual 3-sphere, or if the fundamental group of the ambient space is trivial, then f and g must be isotopic. This generalizes a result of Kosanovic, Schneiderman, and Teichner. The proof is based on the construction of an invariant that classifies the isotopy classes of smooth embeddings of surfaces in ambient 5-dimensional manifolds within a homotopy class, which may be of independent interest. The invariant is defined in terms of the homotopy groups of the 5-dimensional manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07785 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the isotopy classes of embeddings of surfaces in 5-manifolds Qiao, Ruoyu Geometric Topology Let f, g be two homotopic smooth embeddings of a closed surface in a closed oriented 5-dimensional manifold. We show that if f admits a common algebraic dual 3-sphere, or if the fundamental group of the ambient space is trivial, then f and g must be isotopic. This generalizes a result of Kosanovic, Schneiderman, and Teichner. The proof is based on the construction of an invariant that classifies the isotopy classes of smooth embeddings of surfaces in ambient 5-dimensional manifolds within a homotopy class, which may be of independent interest. The invariant is defined in terms of the homotopy groups of the 5-dimensional manifold. |
| title | On the isotopy classes of embeddings of surfaces in 5-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2603.07785 |