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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 onS  3   ×   S  2    . These results are proven using ‘spun embeddings’ and Lefschetz fibrations.

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