Unfaithful complex hyperbolic triangle groups, II: Higher order reflections
نویسندگان
چکیده
منابع مشابه
Unfaithful Complex Hyperbolic Triangle Groups Ii: Higher Order Reeections
We consider symmetric complex hyperbolic triangle groups generated by three complex reeec-tions with angle 2=p. We restrict our attention to those groups where certain words are elliptic. Our goal is to nd necessary conditions for such a group to be discrete. The main application we have in mind is that such groups are candidates for non-arithmetic lattices in SU(2,1).
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A complex hyperbolic triangle group is the group of complex hyperbolic isometries generated by complex involutions fixing three complex lines in complex hyperbolic space. Such a group is called equilateral if there is an isometry of order three that cyclically permutes the three complex lines. We consider equilateral triangle groups for which the product of each pair of involutions and the prod...
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The theory of complex hyperbolic discrete groups is still in its childhood but promises to grow into a rich subfield of geometry. In this paper I will discuss some recent progress that has been made on complex hyperbolic deformations of the modular group and, more generally, triangle groups. These are some of the simplest nontrivial complex hyperbolic discrete groups. In particular, I will talk...
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Complex hyperbolic triangle groups are representations of a hyperbolic (p, q, r) reflection triangle group to the group of holomorphic isometries of complex hyperbolic space H C , where the generators fix complex lines. In this paper, we obtain all the discrete and faithful complex hyperbolic (3, 3, n) triangle groups. Our result solves a conjecture of Schwartz [16] in the case when p = q = 3.
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We first demonstrate a family of isomorphisms between complex hyperbolic triangle groups and outline a systematic approach classifying the groups. Then we describe conditions that determine the discreteness of certain groups, in particular we prove a slightly weaker version of a conjecture given by Schwartz. Finally we collect together a list of known discrete triangle groups and propose some g...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2009
ISSN: 0030-8730
DOI: 10.2140/pjm.2009.239.357