Extending Gromov's optimal systolic inequality

TL;DR

This paper extends Gromov's optimal systolic inequality to a broader class of manifolds with cohomology classes formed by cup products of 2-dimensional classes, advancing geometric inequalities in topology.

Contribution

It provides a natural extension of Gromov's inequality to manifolds with fundamental classes as cup products of 2-dimensional cohomology classes.

Findings

Extended Gromov's inequality to new manifold classes

Identified conditions for optimal systolic inequalities

Enhanced understanding of cohomological contributions to geometry

Abstract

The existence of nontrivial cup products or Massey products in the cohomology of a manifold leads to inequalities of systolic type, but in general such inequalities are not optimal (tight). Gromov proved an {optimal} systolic inequality for complex projective space. We provide a natural extension of Gromov's inequality to manifolds whose fundamental cohomology class is a cup product of 2-dimensional classes.