$N$-dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group
Geometric Topology
2025-09-16 v2
Abstract
Starting with a smooth, non-trivial -dimensional knot , and a beaded -dimensional necklace subordinated to , 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 , generated by inversions on the spheres which are the boundary of the ``beads''. We show that if 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].
Cite
@article{arxiv.2410.15183,
title = {$N$-dimensional beaded necklaces and higher dimensional wild knots, invariant by a Schottky group},
author = {Gabriela Hinojosa and Alberto Verjovsky and Juan Pablo Díaz},
journal= {arXiv preprint arXiv:2410.15183},
year = {2025}
}
Comments
22 pages, 8 figures