2013/07/29 by Hayden, Kyle, Sabloff, Joshua M. · 2 citations
#57M25 #57R17 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1307.7683
This paper explores the relationship between the existence of an exact embedded Lagrangian filling for a Legendrian knot in the standard contact \rr3 and the hierarchy of positive, strongly quasi-positive, and quasi-positive knots. On one hand, results of Eliashberg and especially Boileau and Orevkov show that every Legendrian knot with an exact, embedded Lagrangian filling is quasi-positive. On the other hand, we show that if a knot type is positive, then it has a Legendrian representative with an exact embedded Lagrangian filling. Further, we produce examples that show that strong quasi-positivity and fillability are independent conditions.