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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.05805 |
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| _version_ | 1866914453516189696 |
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| author | Lin, Jianfeng Wu, Yue |
| author_facet | Lin, Jianfeng Wu, Yue |
| contents | We prove that there exist infinitely many embedded tori with a common geometric dual in $T^4\#(S^2\times S^2)$ that are homotopic, diffeomorphic, but not isotopic to each other, even after arbitrary many external stabilizations. These surfaces are obtained by applying the Norman trick to a fixed immersed surface, using non-homotopic tubing arcs. The isotopy classes of these surfaces are distinguished by homotopy classes of the 2-handles (relative to the boundary) in the complement of the image of the $0$- and $1$-handles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05805 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-isotopic surfaces in $T^4\#(S^2\times S^2)$: an example Lin, Jianfeng Wu, Yue Geometric Topology We prove that there exist infinitely many embedded tori with a common geometric dual in $T^4\#(S^2\times S^2)$ that are homotopic, diffeomorphic, but not isotopic to each other, even after arbitrary many external stabilizations. These surfaces are obtained by applying the Norman trick to a fixed immersed surface, using non-homotopic tubing arcs. The isotopy classes of these surfaces are distinguished by homotopy classes of the 2-handles (relative to the boundary) in the complement of the image of the $0$- and $1$-handles. |
| title | Non-isotopic surfaces in $T^4\#(S^2\times S^2)$: an example |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2604.05805 |