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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.22794 |
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| _version_ | 1866910227210698752 |
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| author | Díaz, Juan Pablo Hinojosa, Gabriela Verjovsky, Alberto |
| author_facet | Díaz, Juan Pablo Hinojosa, Gabriela Verjovsky, Alberto |
| contents | We prove that every smooth $n$-dimensional knot in $\mathbb{R}^{n+2}$ can be ambiently isotoped into the Menger $n$-dimensional continuum. In contrast with classical embedding theorems for universal compacta, our construction is explicit and proceeds via cubical models, combining the cubical realization theorem of Boege--Hinojosa--Verjovsky with the affine self-similarity of the Menger continuum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Constructive Cubical Realization of $n$-Dimensional Smooth Knots Inside the Menger $M^{n+2}_n$-continuum Díaz, Juan Pablo Hinojosa, Gabriela Verjovsky, Alberto Geometric Topology 57M30, 54H20, 30F40 We prove that every smooth $n$-dimensional knot in $\mathbb{R}^{n+2}$ can be ambiently isotoped into the Menger $n$-dimensional continuum. In contrast with classical embedding theorems for universal compacta, our construction is explicit and proceeds via cubical models, combining the cubical realization theorem of Boege--Hinojosa--Verjovsky with the affine self-similarity of the Menger continuum. |
| title | A Constructive Cubical Realization of $n$-Dimensional Smooth Knots Inside the Menger $M^{n+2}_n$-continuum |
| topic | Geometric Topology 57M30, 54H20, 30F40 |
| url | https://arxiv.org/abs/2510.22794 |