Stable systolic category of the product of spheres

TL;DR

This paper establishes a relationship between the stable systolic category and real cup-length for products of spheres, and proves its invariance under rational equivalences for certain manifolds, advancing understanding of manifold volume complexity.

Contribution

It proves the equality of stable systolic category and real cup-length for products of spheres and shows invariance under rational equivalences for orientable 0-universal manifolds.

Findings

Stable systolic category equals real cup-length for product of spheres.

Invariance of stable systolic category under rational equivalences.

Provides new insights into volume complexity of manifolds.

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.