We present an atlas of Legendrian knots in standard contact three-space. This gives a
conjectural Legendrian classification for all knots with arc index at most 9, including …

We give a combinatorial description of the Legendrian contact homology algebra associated
to a Legendrian link in $ S^ 1\times S^ 2$ or any connected sum $\#^ k (S^ 1\times S^ 2) …

We develop a close relation between satellites of Legendrian knots in ℝ 3 and the
Chekanov–Eliashberg differential graded algebra of the knot. In particular, we generalize …

THE CONTACT HOMOLOGY OF LEGENDRIAN KNOTS WITH MAXIMAL THURSTON–BENNEQUIN
INVARIANT Steven Sivek 1. Introduction The Chekanov k Page 1 i i i i i i JOURNAL OF …

To a differential graded algebra with coefficients in a noncommutative algebra, by
dualisation we associate an $ A_\infty $-category whose objects are augmentations. This …

In the symplectization of standard contact 3-space, ℝ× ℝ 3, it is known that an orientable
Lagrangian cobordism between a Legendrian knot and itself, also known as an orientable …

Symplectic geometry is a branch of differential geometry that studies symplectic and contact
manifolds and their Lagrangian and Legendrian submanifolds. It originated as a …

In this thesis we apply techniques from the bordered and sutured variants of Floer homology
to study Legendrian knots. First, given a front diagram for a Legendrian knot K in S₃ which …

• For each knot, the non-destabilizable Legendrian representatives are depicted (modulo the
symmetries described below), with their (tb, r), along with the conjectural mountain range. As …