Hyperbolicity of Staked Links and Lower Bounds on Their Volumes

TL;DR

This paper introduces 'charm bracelets', a special class of hyperbolic links in handlebodies, and develops methods to construct infinitely many such links with volume bounds based on their components.

Contribution

It defines charm bracelets, a new subset of staked links, and provides tools to construct infinitely many hyperbolic links with volume bounds.

Findings

Infinite families of hyperbolic links constructed

Lower bounds on volumes established

Tools for analyzing charm bracelets developed

Abstract

We define a class of links in handlebodies called ``charm bracelets," which are a subset of staked links. We provide tools to construct infinitely many such hyperbolic links and bound the corresponding volumes from below in terms of volumes corresponding to the individual charms.