Complex hyperbolic (3,3,n)-triangle groups.
Reads0
Chats0
TLDR
In this article, the authors obtained all the discrete and faithful complex hyperbolic (3,3,n) triangle groups for n ≥ 4n≥4, where n is the number of generators.Abstract:
Let p,q,rp,q,r be positive integers. Complex hyperbolic (p,q,r)(p,q,r) triangle groups are representations of the hyperbolic (p,q,r)(p,q,r) reflection triangle group to the holomorphic isometry group of complex hyperbolic space H2CHℂ2, where the generators fix complex lines. In this paper, we obtain all the discrete and faithful complex hyperbolic (3,3,n)(3,3,n) triangle groups for n≥4n≥4. Our result solves a conjecture of Schwartz in the case when p=q=3p=q=3.read more
Citations
More filters
Journal ArticleDOI
A complex hyperbolic Riley slice
John R. Parker,Pierre Will +1 more
TL;DR: In this article, the authors studied subgroups of groups generated by two noncommuting unipotent maps and showed that the boundary of the quotient orbifold associated to the latter group gives a spherical CR uniformisation of the Whitehead link complement.
Journal ArticleDOI
A complex hyperbolic Riley slice
John R. Parker,Pierre Will +1 more
TL;DR: In this paper, the authors studied subgroups of PU(2,1) generated by two noncommuting unipotent maps A and B whose product AB is also un-commuting, and provided a set of coordinates on U that make it homeomorphic to R2.
Journal ArticleDOI
Spherical CR uniformization of Dehn surgeries of the Whitehead link complement
TL;DR: In this article, the spherical CR Dehn surgery was applied to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures in the complex hyperbolic plane ℍℂ2.
Posted Content
Families of Geometries, Real Algebras, and Transitions
TL;DR: Trettel et al. as discussed by the authors presented a new proof of the theorem of Cooper, Danciger and Wienhard classifying the limits under conjugacy of the orthogonal groups in GL(n;R).
Journal ArticleDOI
Spherical CR Dehn surgeries
TL;DR: In this paper, a three-dimensional cusped spherical CR manifold M can be deformed in such a way that the peripheral holonomy is generated by a nonparabolic element.
References
More filters
Journal Article
Complex hyperbolic ideal triangle groups.
TL;DR: In this article, the Cartan angular invariant is investigated for groups generated by inversions in three mutually asymptotic complex geodesics in complex hyperbolic space.
Posted Content
Complex hyperbolic triangle groups
TL;DR: The theory of complex hyperbolic discrete groups is still in its childhood but promises to grow into a rich subfield of geometry as mentioned in this paper, and some recent progress has been made on complex-hyperbolic deformations of the modular group and, more generally, triangle groups.
Journal ArticleDOI
The shape invariant of triangles and trigonometry in two-point homogeneous spaces
TL;DR: In this article, the authors define a fourth basic invariant, besides the lengths of the three sides of a triangle, which determines a triangle in the complex and quaternion projective spaces ℂP====== nTextColor and ℍP¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ nTextColor (n ≥ 2) uniquely up to isometry.
Journal ArticleDOI
New non-arithmetic complex hyperbolic lattices
TL;DR: In this article, a family of non-arithmetic lattices with commensurable properties was presented, and five distinct classes of commensurability classes were defined for discrete groups acting on complex hyperbolic planes.