Covering Trick and Embolic Volume

TL;DR

This paper explores the relationship between embolic volume and the first Betti number of compact manifolds, utilizing Gromov's covering trick from systolic geometry to establish new insights.

Contribution

It introduces a novel connection between embolic volume and topological invariants using an enhanced version of Berger's covering trick.

Findings

Established a relation between embolic volume and first Betti number.

Provided detailed exposition of Gromov's covering trick.

Extended the application of covering trick in systolic geometry.

Abstract

Embolic volume of compact manifolds is defined in terms of Berger's embolic inequality. In this paper, we show a result of relating embolic volume to the first Betti number. The proof relies on Gromov's covering argument appeared in systolic geometry. Berger called this method covering trick. We exploit and present more details to covering trick in the paper.