On the detection of knotted spheres by their traces in high dimensions
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arXiv
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| Main Authors: | , , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911258015432704 |
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| author | Bais, Valentina Di Prisa, Alessio Hartman, Daniel Hsueh, Chun-Sheng Kegel, Marc Merz, Alice Pencovitch, Mark Ray, Arunima Santoro, Diego Truöl, Paula Wakelin, Laura |
| author_facet | Bais, Valentina Di Prisa, Alessio Hartman, Daniel Hsueh, Chun-Sheng Kegel, Marc Merz, Alice Pencovitch, Mark Ray, Arunima Santoro, Diego Truöl, Paula Wakelin, Laura |
| contents | For every $n \geq 4$, we demonstrate the existence of non-isotopic smooth $(n-2)$-knots in $S^n$ with diffeomorphic traces by generalising the RBG link construction to all dimensions. Conversely, we prove that for every $n \geq 4$, the unknot in $S^n$ is detected by the diffeomorphism type of its surgery and hence by its trace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07251 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the detection of knotted spheres by their traces in high dimensions Bais, Valentina Di Prisa, Alessio Hartman, Daniel Hsueh, Chun-Sheng Kegel, Marc Merz, Alice Pencovitch, Mark Ray, Arunima Santoro, Diego Truöl, Paula Wakelin, Laura Geometric Topology 57K45, 57R65 (primary), 57K40, 57K10, 57R40 (secondary) For every $n \geq 4$, we demonstrate the existence of non-isotopic smooth $(n-2)$-knots in $S^n$ with diffeomorphic traces by generalising the RBG link construction to all dimensions. Conversely, we prove that for every $n \geq 4$, the unknot in $S^n$ is detected by the diffeomorphism type of its surgery and hence by its trace. |
| title | On the detection of knotted spheres by their traces in high dimensions |
| topic | Geometric Topology 57K45, 57R65 (primary), 57K40, 57K10, 57R40 (secondary) |
| url | https://arxiv.org/abs/2511.07251 |