5-21【Xiudi Tang】Affine structures of semitoric integrable systems

It is well known that the moment map of a compact toric integrable system is a Delzant polytope which determines the system. The orbit of the polytope under the integral affine group that is of one-to-one correspondence with the system under fiberwise symplectomorphisms. There is a folklore question whether the singular affine structure on the image of momentum maps still determines a semitoric integrable system. We answer this question negatively and give counterexamples; see arXiv:2401.10881.