The cotangent-bundle Hofer–Zehnder capacity conjecture for non-aspherical manifolds

Let $Q$ be a closed oriented manifold that is not a $K(\pi,1)$. The cotangent-bundle conjecture. Then

$$c_{HZ}^\circ(D^*Q)<\infty$$

and the almost existence property for closed contractible characteristics holds in $D^*Q$. The conjecture proposes that the method using symplectic homology with differential graded coefficients extends from the examples established in the paper to every closed oriented manifold that is not a $K(\pi,1)$; its general validity remains open.