Convergence and divergence of Kleinian punctured torus groups
نویسندگان
چکیده
منابع مشابه
Convergence and divergence of Kleinian punctured torus groups
In this paper we give a necessary and sufficient condition in which a sequence of Kleinian punctured torus groups converges. This result tells us that every exotically convergent sequence of Kleinian punctured torus groups is obtained by the method due to Anderson and Canary (Invent. Math. 1996). Thus we obtain a complete description of the set of points at which the space of Kleinian punctured...
متن کاملOn the Maskit Slice of 4-dimensional Kleinian Punctured Torus Groups
Let Γ be a 3-dimensional Kleinian punctured torus group with accidental parabolics. The deformation space of Γ in the group of Möbius transformations on the 2-sphere is well-known as the Maskit slice of punctured torus groups. In this paper, we study the deformation space of Γ in the group of Möbius transformations on the 3-sphere, where Γ is naturally regarded as a 4-dimensional Kleinian group...
متن کاملThe space of Kleinian punctured torus groups is not locally connected
We show that the space of Kleinian punctured torus groups is not locally connected.
متن کاملThe Space of 4-dimensional Kleinian Punctured Torus Groups without Screw Parabolic Transformations
Let Γ be a 3-dimensional Kleinian punctured torus group with accidental parabolic transformations. The deformation space of Γ in the group of Möbius transformations on the 2-sphere is well-known as the Maskit slice M1,1 of punctured torus groups. In this paper, we study deformations Γ of Γ in the group of Möbius transformations on the 3-sphere such that Γ does not contain screw parabolic transf...
متن کاملThe Classification of Punctured-torus Groups
Thurston’s ending lamination conjecture proposes that a finitelygenerated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends. We present a proof of this conjecture for punctured-torus groups. These are free two-generator Kleinian groups with parabolic commutator, which should be though...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2012
ISSN: 1080-6377
DOI: 10.1353/ajm.2012.0024