On cohomology of Kleinian groups. IV. The Ahlfors-Sullivan construction of holomorphic Eichler integrals

1983 ◽  
Vol 43 (1) ◽  
pp. 51-87 ◽  
Author(s):  
Irwin Kra
Keyword(s):  
Kleinian Groups ◽  
Eichler Integrals

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 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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