Triangulation complexity and systolic volume of hyperbolic manifolds

TL;DR

This paper explores the relationship between systolic volume and triangulation complexity in hyperbolic manifolds, building on Gromov's work linking systolic volume to simplicial volume.

Contribution

It establishes a new connection between systolic volume and triangulation complexity specifically for hyperbolic manifolds, using hyperbolic volume theorems.

Findings

Systolic volume of hyperbolic manifolds relates to triangulation complexity.

The proof utilizes J{ }orgensen and Thurston's hyperbolic volume theorem.

Provides a new perspective on geometric invariants of hyperbolic manifolds.

Abstract

Let $M$ be a closed $n$-manifold with nonzero simplicial volume. A central result in systolic geometry from Gromov is that systolic volume of $M$ is related to its simplicial volume. In this short note, we show that systolic volume of hyperbolic manifolds is related to triangulation complexity. The proof is based on J{\o}rgensen and Thurston's theorem of hyperbolic volume.