Geometry of hyperbolic $3$-manifolds with boundary
نویسندگان
چکیده
منابع مشابه
Small Hyperbolic 3-Manifolds With Geodesic Boundary
We classify the orientable finite-volume hyperbolic 3-manifolds having nonempty compact totally geodesic boundary and admitting an ideal triangulation with at most four tetrahedra. We also compute the volume of all such manifolds, we describe their canonical Kojima decomposition, and we discuss manifolds having cusps. The manifolds built from one or two tetrahedra were previously known. There a...
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 کاملOn deformations of hyperbolic 3–manifolds with geodesic boundary
Let M be a complete finite-volume hyperbolic 3–manifold with compact non-empty geodesic boundary and k toric cusps, and let T be a geometric partially truncated triangulation of M . We show that the variety of solutions of consistency equations for T is a smooth manifold or real dimension 2k near the point representing the unique complete structure on M . As a consequence, the relation between ...
متن کاملConstruction and Recognition of Hyperbolic 3-Manifolds with Geodesic Boundary
We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston’s approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and we discuss consistency and completeness equations. Moreover, building on previous work of Ushijima, we extend Weeks’ tilt formula algorithm, which computes th...
متن کاملHyperbolic manifolds with polyhedral boundary
Let (M, ∂M) be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. We are interested in the following question: Question A Let h be a (non-smooth) metric on ∂M , with curvature K > −1. Is there a unique hyperbolic metric g on M , with convex boundary, such that the induced metric on ∂M is h ? There is also a dual statement: Question B Let h be a (non...
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: Kodai Mathematical Journal
سال: 1994
ISSN: 0386-5991
DOI: 10.2996/kmj/1138040048