Applications of singular connections in symplectic and almost complex geometry

In this paper, we give two direct applications of the theory of singular connections developped by Harvey-Lawson [10]. The first one is a version of Lelong-Poincar'e formula for vector bundle over an almost complex manifold. The second is a convergence theorem for divisors associated to symplectic submanifolds constructed by Auroux in [2]. The case of hypersurfaces was done by Donaldsson in [4].