Wild knots embedded in the Menger Sponge
Geometric Topology
2026-04-24 v2
Abstract
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.
Cite
@article{arxiv.2602.20384,
title = {Wild knots embedded in the Menger Sponge},
author = {Gabriela Hinojosa and Ulises Morales-Fuentes and Rogelio Valdez and Alberto Verjovsky},
journal= {arXiv preprint arXiv:2602.20384},
year = {2026}
}
Comments
24 pages, 13 figures