PreprintarXiv licencearXiv
The elastic figure-eight knot is not planar
Abstract
We prove that every elastic knot in any non-torus twist knot class is not planar. In particular, this disproves a numerically motivated planarity conjecture for elastic figure-eight knots.
Related
- Total eight-colorings of maximal planar graphs of maximum degree six
- Non-migration for planar elastic flows
- Travel time tomography for elliptically anisotropic elastic planar media
- The compress-with-another threshold of Szykuła's Figure 3 family
- On infinite knot families with the same HOMFLYPT polynomial
BibTeX
@misc{miura2026elastic,
title = {{The elastic figure-eight knot is not planar}},
author = {Tatsuya Miura},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32320},
eprint = {2610.32320},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32320},
}
RIS
TY - UNPB
TI - The elastic figure-eight knot is not planar
AU - Tatsuya Miura
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32320
UR - https://arxiv.org/abs/2610.32320
AB - We prove that every elastic knot in any non-torus twist knot class is not planar. In particular, this disproves a numerically motivated planarity conjecture for elastic figure-eight knots.
ER -