Obstructions to decomposable exact Lagrangian fillings
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We study some properties of decomposable exact Lagrangian cobordisms between Legendrian links in R 3 -dimensional space with the standard contact structure. In particular, for any decomposable exact Lagrangian filling L of a Legendrian link K , we may obtain a normal ruling of K which is associated with L . We prove that the associated normal rulings must have even number of clasps. As a result, a Legendrian (4,-(2 n + 5))-torus knot, n is greater than or equal to 0, does not have a decomposable exact Lagrangian filling because it has only one normal ruling and this normal ruling has odd number of clasps.