NON-DISCRETE COMPLEX HYPERBOLIC TRIANGLE GROUPS OF TYPE (n, n,∞; k)

نویسندگان

  • SHIGEYASU KAMIYA
  • JOHN R. PARKER
  • JAMES M. THOMPSON
چکیده

A complex hyperbolic triangle group is a group generated by three complex reflections fixing complex slices (complex geodesics) in complex hyperbolic space. Our purpose in this paper is to improve the result in [3] and to discuss discreteness of complex hyperbolic triangle groups of type (n, n,∞; k).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

COMPLEX HYPERBOLIC (3, 3, n) TRIANGLE GROUPS

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.

متن کامل

Unfaithful complex hyperbolic triangle groups I: Involutions

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...

متن کامل

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).

متن کامل

Complex Hyperbolic Triangle Groups

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...

متن کامل

Arithmeticity 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...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009