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$N$-dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group
- Publication Year :
- 2024
-
Abstract
- Starting with a smooth $n$-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.<br />Comment: 17 pages, 8 figures
- Subjects :
- Mathematics - Geometric Topology
Primary: 57M30, 54H20. Secondary: 30F40
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2410.15183
- Document Type :
- Working Paper