Contact Embeddings in Standard Contact Spheres via Approximately Holomorphic Geometry
Vol. 18 (2011), No. 2, Page 139--154.
Mart\'\i nez Torres, David
Contact Embeddings in Standard Contact Spheres via Approximately Holomorphic Geometry
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Abstract:
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's 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.
Mathematics Subject Classification (2010): Primary 53D35, Secondary 57R40, 53C25.
Received: 2010-09-08
