The symplectic Hadamard question
Symplectic Geometry
2026-07-14 v1
Abstract
We show that a simply connected symplectic manifold admitting a complete nonpositively curved compatible metric is symplectomorphic to R^{2n} with its standard symplectic form. This answers the "symplectic Hadamard question" of McDuff-Salamon in the affirmative.
Cite
@article{arxiv.2607.12940,
title = {The symplectic Hadamard question},
author = {Dan Cristofaro-Gardiner},
journal= {arXiv preprint arXiv:2607.12940},
year = {2026}
}
Comments
some Math/AI aspects around this work are discussed in section 1.1