A systolic inequality for 2-complexes of maximal cup-length and systolic area of groups

TL;DR

This paper extends a systolic inequality to 2-dimensional complexes, leading to improved lower bounds for the systolic area of various groups, including free abelian, surface, and certain 3-manifold groups.

Contribution

It generalizes Guth's systolic inequality to 2-complexes and enhances the lower bounds for the systolic area of a broad class of groups.

Findings

Improved universal lower bounds for systolic area of groups

Extension of systolic inequality to 2-complexes

Applicable to groups with elements of order 2

Abstract

We extend a systolic inequality of Guth for Riemannian manifolds of maximal $\mathbb{Z}_2$ cup-length to piecewise Riemannian complexes of dimension 2. As a consequence we improve the previous best universal lower bound for the systolic area of groups for a large class of groups, including free abelian and surface groups, most of irreducible 3-manifold groups, non-free Artin groups and Coxeter groups (or more generally), groups containing an element of order 2.