Ideal Liouville Domains, a cool gadget

Emmanuel Giroux (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

The purpose of these notes is to describe a convenient packaging for those objects nowadays called Liouville domains but which have been studied formerly under various names such as "symplectic manifolds with restricted contact type boundaries" or "complete convex symplectic manifolds with conical/cylindrical ends" [We, EG, Mc, Ge, La, CFH, Vi, Se, CE]. In this text, the term domain systematically refers to a compact manifold with boundary. Definition 0 (Liouville Domains). A Liouville domain is a domain F endowed with a Liouville form, that is, a 1-form λ satisfying the following two axioms:

Domaines: Mathématiques [math]; Géométrie symplectique [math.SG]

Emmanuel Giroux. Ideal Liouville Domains, a cool gadget. Journal of Symplectic Geometry, 2020, 18 (3), pp.769-790. ⟨10.4310/JSG.2020.v18.n3.a5⟩. ⟨hal-03959610⟩