Embedding all contact 3-manifolds in a fixed contact 5-manifold

Abstract

In this note we observe that one can contact embed all contact 3-manifolds into a Stein fillable contact structure on the twisted $S^3$-bundle over $S^2$ and also into a unique overtwisted contact structure on $S^3\times S^2$. These results are proven using "spun embeddings" and Lefschetz fibrations.

19 pages, 4 figures. Fixed typos, and added references and two figures

References in corpus (2)

• Braided embeddings of contact 3-manifolds in the standard contact 5-sphere
• On some examples and constructions of contact manifolds

Cited by in corpus (4)

• Maximal contact and symplectic structures
• The Legendrian Whitney trick
• On some examples and constructions of contact manifolds
• On open book embedding of contact manifolds in the standard contact sphere