Abstract
We prove the existence of contact submanifolds realizing the Poincare dual of the top Chern class of a complex vector bundle over a closed contact manifold. This result is analogue in the contact categoryto Donaldson's construction of symplectic submanifolds. The main tool in the construction is to show the existence of sequences of sections which are asymptotically holomorphic in an appropiate sense and that satisfya transversalitywith es- timates propertydirectlyin the contact category . The description of the ob- tained contact submanifolds allows us to prove an extension of the Lefschetz hyperplane theorem which completes their topological characterization.
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