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Free groups generated by two unipotent maps

  • Chao Jiang und Baohua Xie ORCID logo EMAIL logo
Veröffentlicht/Copyright: 26. März 2024

Abstract

Let A and B be two unipotent elements of SU ( 2 , 1 ) with distinct fixed points. In [S. B. Kalane and J. R. Parker, Free groups generated by two parabolic maps, Math. Z. 303 2023, 1, Paper No. 9], the authors gave several conditions that guarantee the subgroup A , B is discrete and free by using Klein’s combination theorem. We will improve their conditions by using a variant of Klein’s combination theorem. With the same arguments and the additional assumption that AB is unipotent, we also extend Parker and Will’s condition that guarantees the subgroup A , B is discrete and free in [J. R. Parker and P. Will, A complex hyperbolic Riley slice, Geom. Topol. 21 2017, 6, 3391–3451].

MSC 2020: 22E40; 51M10; 20H10

Communicated by Manfred Droste


Award Identifier / Grant number: 11871202

Award Identifier / Grant number: 12271148

Funding statement: This work was supported by the National Natural Science Foundation of China (Grants No. 11871202, No. 12271148).

Acknowledgements

We would like to thank the anonymous referee, whose insightful suggestions helped improving earlier versions of the manuscript. We thank Wei Liao and Mengqi Yu for several useful discussions.

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Received: 2023-12-05
Published Online: 2024-03-26
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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