# Systole on locally symmetric spaces

## TL;DR

This paper surveys the growth of systoles in arithmetic locally symmetric spaces under congruence coverings and provides simplified proofs for optimal Gromov constants across key symmetric space classes.

## Contribution

It offers new, simplified proofs for the best constants of Gromov related to systole growth in various symmetric spaces.

## Key findings

- Established optimal Gromov constants for several symmetric spaces
- Provided simplified proofs for systole growth bounds
- Analyzed systole behavior under congruence coverings

## Abstract

Here we survey on the growth of systoles of arithmetic locally symmetric spaces under the congruence covering and give simple proofs for the best possible constants of Gromov for several important classes of symmetric spaces.