For , we construct Legendrian embeddings of a surface of genus into which lie in pairwise distinct Legendrian isotopy classes and which all have transverse Reeb chords ( is the conjecturally minimal number of chords). Furthermore, for of the embeddings the Legendrian contact homology DGA does not admit any augmentation over , and hence cannot be linearized. We also investigate these surfaces from the point of view of the theory of generating families. Finally, we consider Legendrian spheres and planes in from a similar perspective.
"Knotted Legendrian surfaces with few Reeb chords." Algebr. Geom. Topol. 11 (5) 2903 - 2936, 2011. https://doi.org/10.2140/agt.2011.11.2903