English

Complete hyperbolic structures in the complement of the Borromean rings

Geometric Topology 2021-12-23 v1

Abstract

In this note, we show the fundamental group of the complement of the Borromean rings in S3\Bbb{S}^3 has exactly two representations in PSL(2,C){\rm PSL}(2,\Bbb{C}) which are faithful, discrete and send meridians into parabolic elements. Using this result we are able to show that Borromean rings admit exactly one hyperbolic structure.

Keywords

Cite

@article{arxiv.2112.11932,
  title  = {Complete hyperbolic structures in the complement of the Borromean rings},
  author = {Angel Cano and Juan Francisco Estrada},
  journal= {arXiv preprint arXiv:2112.11932},
  year   = {2021}
}
R2 v1 2026-06-24T08:27:59.758Z