POSITIVE KNOTS AND LAGRANGIAN FILLABILITY.

This paper explores the relationship between the existence of an exact embedded Lagrangian filling for a Legendrian knot in the standard contact R3 and the hierarchy of positive, strongly quasi-positive, and quasipositive 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. [ABSTRACT FROM AUTHOR]