Ideal Lionville domains, a cool gadget

摘要

Liouvile domains are central objects in symplectic geometry today, but they have unsatisfactory aspects due to the requested choice of Liouville forms and to the non-compactness of their completions. Ideal Liouville domains, in contrast, are compact manifolds with boundary merely equipped with a symplectic form in the interior. Still, their isomorphism classes are in one-to-one correspondence with the deformation classes of usual Liouville domains. They are also very useful to relate contact structures with open books.