Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres
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| Format: | Preprint |
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2025
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| _version_ | 1866915291730018304 |
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| author | Gabai, David Gay, David T. Hartman, Daniel |
| author_facet | Gabai, David Gay, David T. Hartman, Daniel |
| contents | We introduce new methods in pseudo-isotopy and embedding space theory. As an application we introduce an invariant that detects nontrivial loops of embedded 2-spheres in $S^{2} \times S^{2}$ and in connected sums of $S^{2} \times S^{2}$. that cannot be homotoped to a loops of spheres dual to the standard horizontal sphere. In the sequel [GGH], we will use these techniques to expand upon the applicability of the invariant and prove $\operatorname{Diff}^{+}(S^{4})$ has an exotic element. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_12088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres Gabai, David Gay, David T. Hartman, Daniel Geometric Topology 57R35 (Primary) 57R52, 57R50, 57N37 (Secondary) We introduce new methods in pseudo-isotopy and embedding space theory. As an application we introduce an invariant that detects nontrivial loops of embedded 2-spheres in $S^{2} \times S^{2}$ and in connected sums of $S^{2} \times S^{2}$. that cannot be homotoped to a loops of spheres dual to the standard horizontal sphere. In the sequel [GGH], we will use these techniques to expand upon the applicability of the invariant and prove $\operatorname{Diff}^{+}(S^{4})$ has an exotic element. |
| title | Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres |
| topic | Geometric Topology 57R35 (Primary) 57R52, 57R50, 57N37 (Secondary) |
| url | https://arxiv.org/abs/2505.12088 |