Hyperbolicity and Volume of Hyperbolic Bongles

Abstract

We consider a simple but infinite class of staked links known as bongles. We provide necessary and sufficient conditions for these bongles to be hyperbolic. Then, we prove that all balanced hyperbolic $n$-bongles have the same volume and the corresponding volume is an upper bound on the volume of any hyperbolic $n$-bongle for $n$ even. Moreover, all hyperbolic $n$-bongles have volume strictly less than $5n(1.01494\dots )$. We also include explicit volume calculations for all hyperbolic 3-bongles through 6-bongles.

16 pages, 11 figures