Towards a braid theory of codimension 2 contact submanifolds, II

In dimension 3, the theory of codimension 2 contact submanifolds is better known as the transverse knot theory of a contact manifold, a theory which has a complete description in terms of braid theory. In higher dimensions, almost nothing is known, but there is a small (but growing) list of results. I will explain a method developed with A. Kaloti to use open books and lefschetz fibrations to study codimension 2 contact embeddings. I will give a lot of background and present some initial applications and will highlight the similarities to and differences from the analogous story in dimension 3.