Injectivity Radius and Fundamental Group of Hyperbolic 3-Manifolds

TL;DR

This paper establishes a relationship between the injectivity radius of hyperbolic 3-manifolds and the complexity of their fundamental groups, providing an upper bound based on the number of generators.

Contribution

It introduces a new bound linking the injectivity radius to the number of generators of the fundamental group in hyperbolic 3-manifolds.

Findings

Upper bound on injectivity radius in terms of fundamental group generators

Connects geometric properties with algebraic complexity

Advances understanding of hyperbolic 3-manifold geometry

Abstract

We show that there is an upper bound on the injectivity radius of a hyperbolic 3-manifold in terms of the the number of generators of its fundamental group.