منابع مشابه
Arithmeticity, Discreteness and Volume
We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of PSL(2,C). We then examine certain two-generator groups which arise as extremals in various geometric problems in the theory of Kleinian groups, in particular those encountered in efforts to determine the smallest co-volume, the Margulis constant and the minimal distance between el...
متن کاملJørgensen Number and Arithmeticity
The Jørgensen number of a rank-two non-elementary Kleinian group Γ is J(Γ) = inf{|trX − 4|+ |tr[X,Y ]− 2| : 〈X,Y 〉 = Γ}. Jørgensen’s Inequality guarantees J(Γ) ≥ 1, and Γ is a Jørgensen group if J(Γ) = 1. This paper shows that the only torsion-free Jørgensen group is the figure-eight knot group, identifies all non-cocompact arithmetic Jørgensen groups, and establishes a characterization of coco...
متن کاملClassification and Arithmeticity of Toroidal
We classify the minimum volume smooth complex hyperbolic surfaces that admit smooth toroidal compactifications, and we explicitly construct their compactifications. There are five such surfaces and they are all arithmetic, i.e., they are associated with quotients of the ball by an arithmetic lattice. Moreover, the associated lattices are all commensurable. The first compactification, originally...
متن کاملArithmeticity (or not) of Monodromy
In 1974 Griffiths and Schmid [1] asked whether monodromy groups of families of varieties acting on cohomology are arithmetic or not. The problem remains largely open, even for well known explicit examples. One case is that of the the families of Calabi-Yau three-folds, which have received much attention starting with the paper of Candelas-Parks et al. Of the well known 14 such families, 7 are k...
متن کاملArithmeticity of complex hyperbolic triangle groups
Complex hyperbolic triangle groups, originally studied by Mostow in building the first nonarithmetic lattices in PU(2, 1), are a natural generalization of the classical triangle groups. A theorem of Takeuchi states that there are only finitely many Fuchsian triangle groups that determine an arithmetic lattice in PSL2(R), so triangle groups are generically nonarithmetic. We prove similar finiten...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1987
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1987.102149