A remark about weak fillings

摘要

Let L be a closed manifold of dimension n >= 2 which admits a totally real embedding into C-n. Let ST* L be the space of rays of the cotangent bundle T* L of L, and let DT*L be the unit disk bundle of T*L defined by any Riemannian metric on L. We observe that ST* L endowed with its standard contact structure admits weak symplectic fillings W which are diffeomorphic to DT*L and for which any closed Lagrangian sub manifold N C W has the property that the map H-1 (N, R) -> H-1(W, R) has a nontrivial kernel. This relies on a variation on a theorem by Laudenbach and Sikorav.