Contact structures on 5-manifolds

Using recent work on high dimensional Lutz twists and families of Weinstein structures we show that any almost contact structure on a 5-manifold is homotopic to a contact structure.Comment: 18 pages, 1 figure, fixed a potential gap in the proof of the main theorem and added details to clarify certain parts of the argumen

Knots and Contact Geometry

We classify Legendrian torus knots and figure eight knots in the tight contact structure on the 3-sphere up to Legendrian isotopy. As a corollary to this we also obtain the classification of transversal torus knots and figure eight knots up to transversal isotopy