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A Discreteness Condition for Subgroups of $$\mathbf {PU}$$ PU (2,1)

A Discreteness Condition for Subgroups of $$\mathbf {PU}$$ PU (2,1) 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

A Discreteness Condition for Subgroups of $$\mathbf {PU}$$ PU (2,1)

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Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-019-00275-y
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Computational Methods and Function TheorySpringer Journals

Published: May 20, 2019

References