On the systole growth in congruence quaternionic hyperbolic manifolds

TL;DR

This paper establishes an explicit lower bound for the systole in principal congruence covers of compact quaternionic hyperbolic manifolds and proves that this bound is optimal.

Contribution

It provides the first explicit lower bound for systoles in these manifolds and demonstrates its optimality.

Findings

Explicit lower bound for systole in quaternionic hyperbolic manifolds

Proof of the optimality of the lower bound

Advances understanding of geometric properties of these manifolds

Abstract

We provide an explicit lower bound for the sytole in principal congruence covers of compact quaternionic hyperbolic manifolds. We also prove the optimality of this lower bound.