Stable Systolic Category of Manifolds and the Cup-length

TL;DR

This paper investigates the relationship between the stable systolic category and the rational cup-length of manifolds, establishing conditions under which they are equal, especially for simply connected manifolds of dimension less than 8.

Contribution

It proves the equality of stable systolic category and rational cup-length for certain simply connected manifolds, complementing Gromov's lower bound.

Findings

Stable systolic category equals rational cup-length for simply connected manifolds of dimension <8.

The paper establishes the inequality in the opposite direction of Gromov's theorem.

Results contribute to understanding the geometric-topological invariants of manifolds.

Abstract

It follows from a theorem of Gromov that the stable systolic category of a closed manifold is bounded from below by the rational cup-length of the manifold. In the paper we study the inequality in the opposite direction. In particular, combining our results with Gromov's theorem, we prove the equality of stable systolic category and rational cup-length for simply connected manifolds of dimension less than 8.