English

Hyperbolicity and Volume of Hyperbolic Bongles

Geometric Topology 2025-01-07 v1

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 nn-bongles have the same volume and the corresponding volume is an upper bound on the volume of any hyperbolic nn-bongle for nn even. Moreover, all hyperbolic nn-bongles have volume strictly less than 5n(1.01494)5n(1.01494\dots). We also include explicit volume calculations for all hyperbolic 3-bongles through 6-bongles.

Keywords

Cite

@article{arxiv.2501.02360,
  title  = {Hyperbolicity and Volume of Hyperbolic Bongles},
  author = {Colin Adams and Francisco Gomez-Paz and Jiachen Kang and Lukas Krause and Gregory Li and Reyna Li and Chloe Marple and Ziwei Tan},
  journal= {arXiv preprint arXiv:2501.02360},
  year   = {2025}
}

Comments

16 pages, 11 figures