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We establish a sufficient condition for a subgroup $$G=\langle A, B\rangle $$ G = ⟨ A , B ⟩ of $$\mathbf {PU}(2,1)$$ PU ( 2 , 1 ) to be discrete, where the pair of isometries (A, B) is $$\mathbb {C}$$ C -decomposable. This discreteness criterion is a complex hyperbolic version of Gilman’s result in Gilman (Contemp Math 211:261–267, 1997). Furthermore, we give an example to show that one can use our method to ascertain the discreteness of groups that do not pass the classical discreteness test on isometric spheres.
Computational Methods and Function Theory – Springer Journals
Published: May 20, 2019
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