Bounds on Legendrian Double Twist Knots
arXiv:2610.10747
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.