scholarly journals Complex and quaternionic hyperbolic Kleinian groups with real trace fields

2016 ◽  
Vol 93 (1) ◽  
pp. 101-122 ◽  
Author(s):  
Sungwoon Kim ◽  
Joonhyung Kim
Keyword(s):  
Kleinian Groups ◽  
Real Trace ◽  
Trace Fields

scholarly journals A two-dimensional slice through the parameter space of two-generator Kleinian groups

2018 ◽  
Vol 28 (08) ◽  
pp. 1535-1564
Author(s):  
Elena Klimenko ◽  
Natalia Kopteva
Keyword(s):  
Parameter Space ◽  
Kleinian Groups ◽  
Two Dimensional ◽  
Real Trace ◽  
Discreteness Criteria

We describe all real points of the parameter space of two-generator Kleinian groups with a parabolic generator, that is, we describe a certain two-dimensional slice through this space. In order to do this, we gather together known discreteness criteria for two-generator groups with a parabolic generator and present them in the form of conditions on parameters. We complete the description by giving discreteness criteria for groups generated by a parabolic and a [Formula: see text]-loxodromic elements whose commutator has real trace and present all orbifolds uniformized by such groups.

scholarly journals Free vs. locally free Kleinian groups

2019 ◽  
Vol 2019 (746) ◽  
pp. 149-170
Author(s):  
Pekka Pankka ◽  
Juan Souto
Keyword(s):  
Hausdorff Dimension ◽  
Kleinian Group ◽  
Cantor Set ◽  
Cantor Sets ◽  
Kleinian Groups ◽  
The Other ◽  
Limit Set ◽  
Limit Sets ◽  
Other Hand

Abstract We prove that Kleinian groups whose limit sets are Cantor sets of Hausdorff dimension < 1 are free. On the other hand we construct for any ε > 0 an example of a non-free purely hyperbolic Kleinian group whose limit set is a Cantor set of Hausdorff dimension < 1 + ε.

Kleinian groups acting onS 3 which are extensions

1998 ◽  
Vol 3 (4) ◽  
pp. 355-374
Author(s):  
L. Potyagailo
Keyword(s):  
Kleinian Groups
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