The symplectically aspherical positive scalar curvature conjecture

A closed symplectically aspherical manifold is a closed manifold whose symplectic form vanishes on every spherical homology class. The symplectically aspherical positive scalar curvature conjecture. A closed symplectically aspherical manifold cannot support a Riemannian metric of positive scalar curvature. This is proposed as a symplectic analogue of the Gromov–Lawson conjecture; the paper presents supporting results, but the statement remains open.