PreprintCC BY 4.0arXiv
Knots and the Sierpinski Tetrahedron
Abstract
In this paper we prove that there are infinitely many knots that cannot be embedded in the 1-skeletons of the finite iterations of the Sierpinski tetrahedron fractal. We do this by proving that such an embedding induces a sphere decomposition of weight at most 6. There are infinitely many knots with spherewidth greater than this.
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BibTeX
@misc{espinosa2026knots,
title = {{Knots and the Sierpinski Tetrahedron}},
author = {Malors Espinosa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24545},
eprint = {2609.24545},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24545},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Knots and the Sierpinski Tetrahedron
AU - Malors Espinosa
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24545
UR - https://arxiv.org/abs/2609.24545
AB - In this paper we prove that there are infinitely many knots that cannot be embedded in the 1-skeletons of the finite iterations of the Sierpinski tetrahedron fractal. We do this by proving that such an embedding induces a sphere decomposition of weight at most 6. There are infinitely many knots with spherewidth greater than this.
ER -