$N$-dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911151772663808 |
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| author | Hinojosa, Gabriela Verjovsky, Alberto Díaz, Juan Pablo |
| author_facet | Hinojosa, Gabriela Verjovsky, Alberto Díaz, Juan Pablo |
| contents | Starting with a smooth, non-trivial $n$-dimensional knot $K\subset\bS^{n+2}$, and a beaded $n$-dimensional necklace subordinated to $K$, we construct a wild knot with a Cantor set of wild points (\ie the knot is not locally flat in these points). The construction uses the conformal Schottky group acting on $\bS^{n+2}$, generated by inversions on the spheres which are the boundary of the ``beads''. We show that if $K$ is a fibered knot, then the wild knot is also fibered. We also study cyclic branched coverings along the wild knots. This work generalizes the result presented in [8]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15183 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $N$-dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group Hinojosa, Gabriela Verjovsky, Alberto Díaz, Juan Pablo Geometric Topology Primary: 57M30, 54H20. Secondary: 30F40 Starting with a smooth, non-trivial $n$-dimensional knot $K\subset\bS^{n+2}$, and a beaded $n$-dimensional necklace subordinated to $K$, we construct a wild knot with a Cantor set of wild points (\ie the knot is not locally flat in these points). The construction uses the conformal Schottky group acting on $\bS^{n+2}$, generated by inversions on the spheres which are the boundary of the ``beads''. We show that if $K$ is a fibered knot, then the wild knot is also fibered. We also study cyclic branched coverings along the wild knots. This work generalizes the result presented in [8]. |
| title | $N$-dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group |
| topic | Geometric Topology Primary: 57M30, 54H20. Secondary: 30F40 |
| url | https://arxiv.org/abs/2410.15183 |