On the Complexity and Volume of Hyperbolic 3-Manifolds

TL;DR

This paper explores the relationship between the volume of hyperbolic 3-manifolds and the complexity of their fundamental groups, providing insights into their geometric and algebraic properties.

Contribution

It introduces a comparative analysis between hyperbolic volume and group complexity, highlighting new connections in 3-manifold topology.

Findings

Volume and group complexity are closely related in hyperbolic 3-manifolds.

New bounds linking volume to fundamental group complexity.

Insights into the structure of hyperbolic 3-manifolds based on algebraic invariants.

Abstract

We compare the volume of a hyperbolic 3-manifold $M$ of finite volume and the complexity of its fundamental group.