Georgia Institute of Technology College of Sciences

In this talk we consider the contact embeddings of contact 3-manifolds to S^5 with the standard contact structure.Every closed 3-manifold can be embedded to S^5 smoothly by Wall's theorem. The only known necessary condition to a contact embedding to the standard S^5 is the triviality of the Euler class of the contact structure. On the other hand there are not so much examples of contact embeddings.I will explain the systematic construction of contact embeddings of some contact structures (containing non Stein fillable ones) on torus bundles and Lens spaces.If time permits I will explain relation between above construction and some polynomials on \mathbb C^3.