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Bounds on Legendrian Double Twist Knots
Abstract
We study Legendrian realizations of double twist knots in the standard tight contact 3-sphere. For the family K(4,m), we give upper bounds on the number of oriented and unoriented Legendrian isotopy classes of maximal Thurston--Bennequin representatives. The proof uses bypass techniques in convex surface theory and the classification of tight contact structures.
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BibTeX
@misc{foldvari2026bounds,
title = {{Bounds on Legendrian Double Twist Knots}},
author = {Viktória Földvári and Vera Vértesi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10747},
eprint = {2610.10747},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10747},
}
RIS
TY - UNPB
TI - Bounds on Legendrian Double Twist Knots
AU - Viktória Földvári
AU - Vera Vértesi
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10747
UR - https://arxiv.org/abs/2610.10747
AB - We study Legendrian realizations of double twist knots in the standard tight contact 3-sphere. For the family K(4,m), we give upper bounds on the number of oriented and unoriented Legendrian isotopy classes of maximal Thurston--Bennequin representatives. The proof uses bypass techniques in convex surface theory and the classification of tight contact structures.
ER -