Wild knots embedded in the Menger Sponge
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913056205832192 |
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| author | Hinojosa, Gabriela Morales-Fuentes, Ulises Valdez, Rogelio Verjovsky, Alberto |
| author_facet | Hinojosa, Gabriela Morales-Fuentes, Ulises Valdez, Rogelio Verjovsky, Alberto |
| contents | In this paper, we provide explicit recursive constructions of infinitely many non-equivalent wild knots contained in the Menger sponge, in such a way that we can control their set of wild points that lies in a usual Cantor set contained in the Menger sponge. Furthermore, we show that wild knots of dynamically defined type arising from Kleinian group actions can be isotoped into the sponge. We want to emphasize that our approach is constructive and geometric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20384 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wild knots embedded in the Menger Sponge Hinojosa, Gabriela Morales-Fuentes, Ulises Valdez, Rogelio Verjovsky, Alberto Geometric Topology 57M30, 54H20, 30F40 In this paper, we provide explicit recursive constructions of infinitely many non-equivalent wild knots contained in the Menger sponge, in such a way that we can control their set of wild points that lies in a usual Cantor set contained in the Menger sponge. Furthermore, we show that wild knots of dynamically defined type arising from Kleinian group actions can be isotoped into the sponge. We want to emphasize that our approach is constructive and geometric. |
| title | Wild knots embedded in the Menger Sponge |
| topic | Geometric Topology 57M30, 54H20, 30F40 |
| url | https://arxiv.org/abs/2602.20384 |