English

$N$-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 nn-dimensional knot K\bSn+2K\subset\bS^{n+2}, and a beaded nn-dimensional necklace subordinated to KK, 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 \bSn+2\bS^{n+2}, generated by inversions on the spheres which are the boundary of the ``beads''. We show that if KK 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].

Keywords

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