Configuration Spaces of Points on the Circle and Hyperbolic Dehn Fillings, Ii
نویسندگان
چکیده
In our previous paper, we discussed the hyperbolization of the configuration space of n (≥ 5) marked points with weights in the projective line up to projective transformations. A variation of the weights induces a deformation. It was shown that this correspondence of the set of the weights to the Teichmüller space when n = 5 and to the Dehn filling space when n = 6 is locally one-to-one near the equal weight. In this paper, we establish its global injectivity.
منابع مشابه
Configuration Spaces of Points on the Circle and Hyperbolic Dehn Fillings
A purely combinatorial compactification of the configuration space of n (≥ 5) distinct points with equal weights in the real projective line was introduced by M. Yoshida. We geometrize it so that it will be a real hyperbolic cone-manifold of finite volume with dimension n − 3. Then, we vary weights for points. The geometrization still makes sense and yields a deformation. The effectivity of def...
متن کاملBounds on Exceptional Dehn Filling Ii
We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.
متن کاملA ug 1 99 7 NONHYPERBOLIC DEHN FILLINGS ON HYPERBOLIC 3 - MANIFOLDS Mario
In this paper we will give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and ∂-reducible. A manifold in the second family has boundary consisting of two tori, and admits two reducible Dehn fillings. A manifo...
متن کاملOn Hyperbolic 3-manifolds Realizing the Maximal Distance between Toroidal Dehn Fillings
For a hyperbolic 3-manifold M with a torus boundary component, all but finitely many Dehn fillings on the torus component yield hyperbolic 3manifolds. In this paper, we will focus on the situation where M has two exceptional Dehn fillings, both of which yield toroidal manifolds. For such situation, Gordon gave an upper bound for the distance between two slopes of Dehn fillings. In particular, i...
متن کاملDehn filling of cusped hyperbolic 3-manifolds with geodesic boundary
We define for each g > 2 and k > 0 a set Mg,k of orientable hyperbolic 3manifolds with k toric cusps and a connected totally geodesic boundary of genus g. Manifolds in Mg,k have Matveev complexity g+k and Heegaard genus g+1, and their homology, volume, and Turaev-Viro invariants depend only on g and k. In addition, they do not contain closed essential surfaces. The cardinality of Mg,k for a fix...
متن کامل