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

Eugenio Borghini

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arXiv · 1909.12720

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

Eugenio Borghini

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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.

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Eugenio Borghini. 2019-09-27. A systolic inequality for 2-complexes of maximal cup-length and systolic area of groups. https://arxiv.org/abs/1909.12720

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