Stable systolic category of manifolds and the cup-length

Abstract.

It follows from a theorem of Gromov that the stable systolic category ${\rm cat}_{\rm stsys} M$ of a closed manifold M is bounded from below by ${\rm cl}_{\mathbb{Q}} M$, the rational cup-length of M [Ka07]. We study the inequality in the opposite direction. In particular, combining our results with Gromov’s theorem, we prove the equality ${\rm cat}_{\rm stsys} M = {\rm cl}_{\mathbb{Q}} M$ for simply connected manifolds of dimension ≤ 7.