منابع مشابه
On Neoclassical Schottky Groups
The goal of this paper is to describe a theoretical construction of an infinite collection of non-classical Schottky groups. We first show that there are infinitely many non-classical noded Schottky groups on the boundary of Schottky space, and we show that infinitely many of these are “sufficiently complicated”. We then show that every Schottky group in an appropriately defined relative conica...
متن کاملAll Fuchsian Schottky groups are classical Schottky groups
Not all Schottky groups of Möbius transformations are classical Schottky groups. In this paper we show that all Fuchsian Schottky groups are classical Schottky groups, but not necessarily on the same set of generators. AMS Classification 20H10; 30F35, 30F40
متن کاملUniformization by Classical Schottky Groups
Koebe’s Retrosection Theorem [8] states that every closed Riemann surface can be uniformized by a Schottky group. In [10] Marden showed that non-classical Schottky groups exist, and a first explicit example of a non-classical Schottky group was given by Yamamoto in [14]. Work on Schottky uniformizations of surfaces with certain symmetry has been done by people such as Hidalgo [7]. The natural q...
متن کاملBoundaries for two - parabolic Schottky groups
The problem can be formulated in a number of equivalent different settings: in 7 terms of the topology and the geometry of hyperbolic three-manifolds, in purely alge8 braic terms, or in a combination of these. Since each of these use terminology that has 9 whose exact meaning has evolved over time, we survey some of the basic terminology 10 for Schottky groups, non-separating disjoint circle gr...
متن کاملKleinian groups of small Hausdorff dimension are classical Schottky groups
Let H be the hyperbolic 3-space. A subgroup Γ of PSL(2,C) = Iso(H) is called a Kleinian group if it is discrete. Let x ∈ H. The orbit of x under action of Γ is denoted by Γx. The limit set ΛΓ of Γ is definited as ΛΓ = Γx ∩ ∂H. By definition, ΛG is smallest closed Γ-invariant subset of ∂H. The group Γ is called second kind if ΛΓ 6= ∂H, otherwise it is said to be first kind. The set ΩΓ = ∂H 3 − Λ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03792-x