A Systolic Inequality for 2-Complexes of Maximal Cup-Length and Systolic Area of Groups

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.