Starting from a Liouville 1-form on a surface, we have been led to 3-dimensional contact geometry, and convex surfaces. We now go in the other direction.
(Technical) We’re going to take Liouville structures and move them into 3 dimensions, to obtain contact structures.
(Technical) I’d like to show you some very nice geometry, involving some vector fields and differential forms.
Fun with a number, or two, or four. An interesting complex complexity.
Basic results and the power of convex surfaces.
Details on the significance of the paper, overtwisted discs, characteristic foliations, and contact structures.
My attempt to flesh out a few of the details.
Based on Casson and Bleiler’s book.