THE LEGENDRIAN KNOT ATLAS WUTICHAI CHONGCHITMATE AND LENHARD NG

to accompany the paper “An atlas of Legendrian knots ” by the authors [2]. This file was last changed on 14 August 2013. The table on the following pages depicts conjectural classifications of Leg-endrian knots in all prime knot types of arc index up to 9. For each knot, we present a conjecturally complete list of non-destabilizable Legendrian rep-resentatives, modulo the symmetries of orientation reversal L 7 → −L and Legendrian mirroring L 7 → µ(L). As usual, rotate 45 ◦ counterclockwise to translate from grid diagrams to fronts. Each knot also comes with its conjectural Legendrian mountain range (extending infinitely downwards), comprised of black and red dots, plot-ted according to their Thurston–Bennequin number (vertical) and rotation number (horizontal). Arrows represent positive and negative Legendrian stabilization. The values of (tb, r) are not labeled but can be deduced from the values given for the non-destabilizable representatives. Boxes surround values of (tb, r) that have, or appear to have, more than one Legendrian rep-resentative, and mountain ranges without boxes represent knot types that are conjecturally Legendrian simple. The dots represent conjecturally dis-tinct Legendrian isotopy classes; black dots are provably distinct classes, while red dots are conjecturally but not provably distinct from the black dots and each other. Thus the black dots represent a lower bound for the Legendrian mountain range, and the totality of dots represent our current best guess for the precise mountain range (which however could theoretically be larger or smaller than what is depicted). Legendrian knots have been classified for several knot types, including torus knots and 41 [3] and twist knots [4]. These comprise the knots 31, 41