The conjecture that exotic tori admit no symplectic structures

An exotic torus is a smooth closed manifold homeomorphic to a torus but not diffeomorphic to it. A symplectic structure on a smooth manifold is a closed, nondegenerate differential $2$-form.

Exotic tori carry no symplectic structures. There are no symplectic structures on exotic tori.

This is the symplectic analogue of the Benson–Gordon problem concerning Kähler structures on exotic tori. The paper presents partial negative results and related evidence, but does not establish the conjecture in general.