Hyperbolic Structures on 3-manifolds, I: Deformation of Acylindrical Manifolds
نویسنده
چکیده
This is an eprint approximation to [Thu86], which is the definitive form of this paper. This eprint is provided for convenience only; the theorem numbering of this version is different, and not all corrections are present, so any reference or quotation should refer to the published form. Parts II and III ( [Thua] and [Thub]) of this series, although accepted for publication, for many years have only existed in preprint form; they will also be made available as eprints.
منابع مشابه
References for Geometrization Seminar References
[1] L. Ahlfors and L. Bers, Riemann’s mapping theorem for variable metrics, Ann. Math. 72 (1960), pp. 413– 429 [2] F. Bonahon, Bouts des variétés hyperboliques de dimension 3, Ann. Math. 124 (1986), pp. 71–158 [3] D. Epstein and A. Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, in Analytical and Geometric Aspects of Hyperbolic Space, LMS 111 (198...
متن کاملHyperbolic Structures on 3-manifolds, Iii: Deformations of 3-manifolds with Incompressible Boundary
This is the third in a series of papers construting hyperbolic structures on Haken manifolds, analyzing the mixed case of 3-manifolds that with incompressible boundary that are not acylindrical, but are also not interval bundles. The main ingredient (beyond [Thu86] and [Thu98] is an upper bound for the hyperbolic length of the ‘window frame’, that is, the boundaries of I-bundles in the manifold...
متن کاملLower Bounds on Volumes of Hyperbolic Haken 3-manifolds
In this paper, we find lower bounds for the volumes of certain hyperbolic Haken 3manifolds. The theory of Jorgensen and Thurston shows that the volumes of hyperbolic 3-manifolds are well-ordered, but no one has been able to find the smallest one. The best known result for closed manifolds is that the smallest closed hyperbolic 3-manifold has volume > 0.16668, proven by Gabai, Meyerhoff, and Thu...
متن کاملGeodesic planes in the convex core of an acylindrical 3-manifold
Let M be a convex cocompact, acylindrical hyperbolic 3-manifold of infinite volume, and let M∗ denote the interior of the convex core of M . In this paper we show that any geodesic plane inM∗ is either closed or dense. We also show that only countably many planes are closed. These are the first rigidity theorems for planes in convex cocompact 3-manifolds of infinite volume that depend only on t...
متن کاملThe deformation theory of hyperbolic cone-3-manifolds with cone-angles less than 2π
This is the first in a series of two papers in which we develop the deformation theory of hyperbolic cone-3-manifolds with cone-angles less than 2π, i.e. contained in the interval (0, 2π). In the present paper we focus on deformations keeping the topological type of the conemanifold fixed.
متن کامل