Finitely Generated Kleinian Groups

1982 ◽  
pp. 273-289
Author(s):  
Lars V. Ahlfors
Keyword(s):  
Kleinian Groups ◽  
Finitely Generated

scholarly journals Commensurators of finitely generated nonfree Kleinian groups

2011 ◽  
Vol 11 (1) ◽  
pp. 605-624 ◽  
Author(s):  
Christopher Leininger ◽  
Darren D Long ◽  
Alan W Reid
Keyword(s):  
Kleinian Groups ◽  
Finitely Generated

scholarly journals On Periods of Meromorphic Eichler Integrals

1975 ◽  
Vol 57 ◽  
pp. 1-26
Author(s):  
Hiroki Sato
Keyword(s):  
Fuchsian Group ◽  
Kleinian Groups ◽  
Cohomology Groups ◽  
Finitely Generated ◽  
Eichler Integrals

In this paper we treat cohomology groups H1(G, C2q-1, M) of meromorphic Eichler integrals for a finitely generated Fuchsian group G of the first kind. According to L. V. Ahlfors [2] and L. Bers [4], H1(G, C2q-1, M) is the space of periods of meromorphic Eichler integrals for G. In the previous paper [8], we had period relations and inequalities of holomorphic Eichler integrals for a certain Kleinian groups.

scholarly journals A Fréchet law and an Erdős–Philipp law for maximal cuspidal windings

2012 ◽  
Vol 33 (4) ◽  
pp. 1008-1028 ◽  
Author(s):  
JOHANNES JAERISCH ◽  
MARC KESSEBÖHMER ◽  
BERND O. STRATMANN
Keyword(s):  
Extreme Value Theory ◽  
Continued Fractions ◽  
Geodesic Flow ◽  
Fuchsian Group ◽  
Value Theory ◽  
Extreme Value ◽  
Kleinian Groups ◽  
Riemannian Surface ◽  
Finitely Generated

AbstractIn this paper we establish a Fréchet law for maximal cuspidal windings of the geodesic flow on a Riemannian surface associated with an arbitrary finitely generated, essentially free Fuchsian group with parabolic elements. This result extends previous work by Galambos and Dolgopyat and is obtained by applying extreme value theory. Subsequently, we show that this law gives rise to an Erdős–Philipp law and to various generalized Khintchine-type results for maximal cuspidal windings. These results strengthen previous results by Sullivan, Stratmann and Velani for Kleinian groups, and extend earlier work by Philipp on continued fractions, which was inspired by a conjecture of Erdős.

scholarly journals CANNON–THURSTON MAPS FOR KLEINIAN GROUPS

2017 ◽  
Vol 5 ◽  
Author(s):  
MAHAN MJ
Keyword(s):  
Free Groups ◽  
Kleinian Groups ◽  
Surface Groups ◽  
Finitely Generated ◽  
Ending Lamination

We show that Cannon–Thurston maps exist for degenerate free groups without parabolics, that is, for handlebody groups. Combining these techniques with earlier work proving the existence of Cannon–Thurston maps for surface groups, we show that Cannon–Thurston maps exist for arbitrary finitely generated Kleinian groups without parabolics, proving conjectures of Thurston and McMullen. We also show that point pre-images under Cannon–Thurston maps for degenerate free groups without parabolics correspond to endpoints of leaves of an ending lamination in the Masur domain, whenever a point has more than one pre-image. This proves a conjecture of Otal. We also prove a similar result for point pre-images under Cannon–Thurston maps for arbitrary finitely generated Kleinian groups without parabolics.

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