Free groups generated by two screw parabolic maps

In this paper, we provide sufficient conditions for groups generated by two screw parabolic maps of PU ( 2 , 1 ) with distinct fixed points to be discrete and free. As an example, we apply our results to the classical group ⟨ g θ , f θ ⟩ constructed in Gusevskii, N., Parker, J.R.: Representations of...

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Veröffentlicht in:	Geometriae dedicata 2024-12, Vol.218 (6), Article 107
Hauptverfasser:	Liao, Wei, Xie, Baohua
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebraic Geometry Convex and Discrete Geometry Differential Geometry Hyperbolic coordinates Hyperbolic Geometry Mathematics Mathematics and Statistics Original Paper Projective Geometry Topology
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Zusammenfassung:	In this paper, we provide sufficient conditions for groups generated by two screw parabolic maps of PU ( 2 , 1 ) with distinct fixed points to be discrete and free. As an example, we apply our results to the classical group ⟨ g θ , f θ ⟩ constructed in Gusevskii, N., Parker, J.R.: Representations of free Fuchsian groups in complex hyperbolic space. Topology 39, 33–60 (2000).
ISSN:	0046-5755 1572-9168
DOI:	10.1007/s10711-024-00958-4