Systolic volume of homology classes

TL;DR

This paper explores the systolic volume as a numerical invariant that measures the geometric realization of homology classes in finitely presentable groups, revealing its utility in understanding topological properties.

Contribution

It investigates the properties of systolic volume, demonstrating its effectiveness as a tool for analyzing topological features of homology classes in finitely presentable groups.

Findings

Systolic volume is a complex invariant that encodes topological information.

It provides new insights into the geometric realization of homology classes.

The study highlights the invariant's potential in topological investigations.

Abstract

Given an integer homology class of a finitely presentable group, the systolic volume quantifies how tight could be a geometric realization of this class. In this paper, we study various aspects of this numerical invariant showing that it is a complex and powerful tool to investigate topological properties of homology classes of finitely presentable groups.