Classification of parabolic generating pairs of Kleinian groups with two parabolic generators

Shunsuke Aimi; Donghi Lee; Shunsuke Sakai; Makoto Sakuma

Classification of parabolic generating pairs of Kleinian groups with two parabolic generators

Geometric Topology 2020-08-05 v2

Authors: Shunsuke Aimi , Donghi Lee , Shunsuke Sakai , Makoto Sakuma

Abstract

We give an alternative proof to Agol's classification of parabolic generating pairs of non-free Kleinian groups generated by two parabolic transformations. As an application, we give a complete characterisation of epimorphims between $2$ -bridge knot groups and a complete characterisation of degree one maps between the exteriors of hyperbolic $2$ -bridge links.

Keywords

kleinian groups parabolic generators classification 2-bridge knot groups epimorphisms hyperbolic links

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@article{arxiv.2001.11662,
  title  = {Classification of parabolic generating pairs of Kleinian groups with two parabolic generators},
  author = {Shunsuke Aimi and Donghi Lee and Shunsuke Sakai and Makoto Sakuma},
  journal= {arXiv preprint arXiv:2001.11662},
  year   = {2020}
}

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28 pages, 9 figures

Classification of parabolic generating pairs of Kleinian groups with two parabolic generators

Abstract

Keywords

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