Contact Embeddings in Standard Contact Spheres via Approximately Holomorphic Geometry

We generalize the work of A. Mori using approximately holomorphic methods to show that any closed co-oriented contact manifold of dimension 2n + 1 admits contact embeddings in the standard contact sphere of dimension 4n + 3. This also recovers results of M. Gromov but without appealing to an h-principle. Our construction also extends Mori\u27s in being compatible with the open book decompositions carrying contact structures as introduced by E. Giroux. Therefore our work provides a unified setting for contact embeddings and open book decompositions for closed co-oriented contact manifolds. We also remark on the properties of the pages of the open book decompositions