# Hyperbolicity of links complements in Seifert fibered spaces

## TL;DR

This paper proves that the complement of certain links in Seifert fibered spaces admits a finite-volume hyperbolic structure and provides bounds on its volume, extending understanding of 3-manifold geometries.

## Contribution

It establishes conditions under which link complements in Seifert fibered spaces are hyperbolic and offers combinatorial volume bounds, a novel result in 3-manifold topology.

## Key findings

- Link complements admit finite-volume hyperbolic structures.
- Provides combinatorial bounds for the volume of these hyperbolic manifolds.
- Extends hyperbolicity results to links in Seifert fibered spaces.

## Abstract

Let $\bar\gamma$ be a link in a Seifert fibered space $M$ over a hyperbolic $2$-orbifolds $\mathcal O$ that projects injectively to a filling multicurve of closed geodesics $\gamma$ in $\mathcal O.$ We prove that the complement $M_{\bar\gamma}$ of $\bar\gamma$ in $M$ admits a hyperbolic structure of finite volume and give combinatorial bounds of its volume.