Wild knots embedded in the Menger Sponge

Fuente: arXiv
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Hauptverfasser: Hinojosa, Gabriela, Morales-Fuentes, Ulises, Valdez, Rogelio, Verjovsky, Alberto
Format: Preprint
Veröffentlicht: 2026
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author Hinojosa, Gabriela
Morales-Fuentes, Ulises
Valdez, Rogelio
Verjovsky, Alberto
author_facet Hinojosa, Gabriela
Morales-Fuentes, Ulises
Valdez, Rogelio
Verjovsky, Alberto
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2602_20384
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Wild knots embedded in the Menger Sponge
Hinojosa, Gabriela
Morales-Fuentes, Ulises
Valdez, Rogelio
Verjovsky, Alberto
Geometric Topology
57M30, 54H20, 30F40
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.
title Wild knots embedded in the Menger Sponge
topic Geometric Topology
57M30, 54H20, 30F40
url https://arxiv.org/abs/2602.20384