Stable systolic category of the product of spheres

Abstract

The stable systolic category of a closed manifold $M$ indicates the complexity in the sense of volume. This is a homotopy invariant, even though it is defined by some relations between homological volumes on $M$. We show an equality of the stable systolic category and the real cup-length for the product of arbitrary finite dimensional real homology spheres. Also we prove the invariance of the stable systolic category under the rational equivalences for orientable $0$–universal manifolds.