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## Cohomology of toric origami manifolds with acyclic proper faces

Journal of Symplectic Geometry. 2017. Vol. 15. No. 3. P. 645-685.
Ayzenberg A., Masuda M., Park S., Zeng H.

A toric origami manifold is a generalization of a symplectic toric manifold (or a toric symplectic manifold). The origami symplectic form is allowed to degenerate in a good controllable way in contrast to the usual symplectic form. It is widely known that symplectic toric manifolds are encoded by Delzant polytopes, and the cohomology and equivariant cohomology rings of a symplectic toric manifold can be described in terms of the corresponding polytope. Recently, Holm and Pires described the cohomology of a toric origami manifold $M/T$ when