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

Shunsuke Aimi; Donghi Lee; Shunsuke Sakai; Makoto Sakuma

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arXiv · 2001.11662

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

Shunsuke Aimi·Donghi Lee·Shunsuke Sakai·Makoto Sakuma

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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.

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Shunsuke Aimi, Donghi Lee, Shunsuke Sakai, Makoto Sakuma. 2020-01-31. Classification of parabolic generating pairs of Kleinian groups with two parabolic generators. https://arxiv.org/abs/2001.11662

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