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Hyperbolicity and Volume of Hyperbolic Bongles

Authors :
Adams, Colin
Gomez-Paz, Francisco
Kang, Jiachen
Krause, Lukas
Li, Gregory
Li, Reyna
Marple, Chloe
Tan, Ziwei
Publication Year :
2025

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.<br />Comment: 16 pages, 11 figures

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2501.02360
Document Type :
Working Paper