Journal of Symplectic Geometry

Volume 18 (2020)

Number 3

Ideal Liouville Domains, a cool gadget

Pages: 769 – 790



Emmanuel Giroux (Département Mathématiques et Applications, École Normale Supérieure, Paris, France)


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.

Partially supported by the ANR grant MICROLOCAL (ANR-15CE40-0006).

Received 19 March 2018

Accepted 16 July 2019

Published 30 July 2020