Journal of Symplectic Geometry
Volume 17 (2019)
Presymplectic convexity and (ir)rational polytopes
Pages: 1479 – 1511
In this paper, we extend the Atiyah–Guillemin–Sternberg convexity theorem and Delzant’s classification of symplectic toric manifolds to presymplectic manifolds. We also define and study the Morita equivalence of presymplectic toric manifolds and of their corresponding framed momentum polytopes, which may be rational or non-rational. Toric orbifolds , quasifolds  and noncommutative toric varieties  may be viewed as the quotient of our presymplectic toric manifolds by the kernel isotropy foliation of the presymplectic form.
The first author was partially supported by the National Natural Science Foundation of China grant number 11871334 and by NCCR SwissMAP grant of the Swiss National Science Foundation.
Received 4 June 2017
Accepted 5 September 2018
Published 20 November 2019