Exotic families of embeddings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916651673321472 |
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| author | Auckly, Dave Ruberman, Daniel |
| author_facet | Auckly, Dave Ruberman, Daniel |
| contents | We construct a number of topologically trivial but smoothly non-trivial families of embeddings of 3-manifolds in 4-manifolds. These include embeddings of homology spheres in $S^4$ that are not isotopic but have diffeomorphic complements, and families (parameterized by high-dimensional spheres) of embeddings of any 3-manifold that embeds in a blown-up K3 surface. In each case, the families are constructed so as to be topologically trivial in an appropriate sense. We also illustrate a general technique for converting a non-trivial family of embeddings into a non-trivial family of submanifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exotic families of embeddings Auckly, Dave Ruberman, Daniel Geometric Topology 57K41 (primary), 57N37 (secondary) We construct a number of topologically trivial but smoothly non-trivial families of embeddings of 3-manifolds in 4-manifolds. These include embeddings of homology spheres in $S^4$ that are not isotopic but have diffeomorphic complements, and families (parameterized by high-dimensional spheres) of embeddings of any 3-manifold that embeds in a blown-up K3 surface. In each case, the families are constructed so as to be topologically trivial in an appropriate sense. We also illustrate a general technique for converting a non-trivial family of embeddings into a non-trivial family of submanifolds. |
| title | Exotic families of embeddings |
| topic | Geometric Topology 57K41 (primary), 57N37 (secondary) |
| url | https://arxiv.org/abs/2501.12673 |