Hyperbolicity and Volume of Hyperbolic Bongles

Colin Adams; Francisco Gomez-Paz; Jiachen Kang; Lukas Krause; Gregory Li; Reyna Li; Chloe Marple; Ziwei Tan

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arXiv · 2501.02360

Hyperbolicity and Volume of Hyperbolic Bongles

Colin Adams·Francisco Gomez-Paz·Jiachen Kang·Lukas Krause·Gregory Li·Reyna Li·Chloe Marple·Ziwei Tan

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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.

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BibTeX RIS

Colin Adams, Francisco Gomez-Paz, Jiachen Kang, Lukas Krause, Gregory Li, Reyna Li, Chloe Marple, Ziwei Tan. 2025-01-04. Hyperbolicity and Volume of Hyperbolic Bongles. https://arxiv.org/abs/2501.02360

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