Orderability in contact manifolds

Given a variety of contact M, a subvariety L is said Legendriana if it is tangent to the contact distribution and has maximum dimension (the maximum dimension is conditioned by the condition of being tangent to the contact distribution). Note by Leg (L) the space of Isotope Legendrianas subvarieties to L.Y. Eliashberg and L. Polterovich conducted a study on the manageability of the contactomorphism groups that allowed us to find a relationship between the orderliness of the Leg (L) space and the existence of positive Legendrian ties. This relationship is extensible to the universal Leg (L) coater as long as we consider that the previous ties are also contractile. Positive links of contactomorphisms are constructed in Legendrian subvarieties in different cases. In particular, we partially recover the result of G. Liu, who affirms that every Legendriana Loose variety admits a positive bond, assuming that certain little restrictive topological properties on the Legendriana subvariety are met. Moreover, the contractibility of ties is proved by assuming an extra topological property