Quasi-fuchsian structures on hyperbolic 3-manifolds admitting a decomposition into ideal tetrahedra
type: Item
instance of: scholarly article
title: Quasi-fuchsian structures on hyperbolic 3-manifolds admitting a decomposition into ideal tetrahedra
zbMATH Open document ID: 0868.57020
DOI: 10.1007/BF01195711
published in: Archiv der Mathematik
publication date: 1997-08-18T00:00:00Z
review text: This work aims at quasi-Fuchsian structures on hyperbolic 3-manifolds. They were first studied by \textit{W. P. Thurston} [The geometry and topology of three-manifolds, Princeton Univ. Maths. Dept. Notes (1979)] where he started with a hyperbolic link \(L\) in \(S^3\). He had shown that infinitely many of the manifolds obtained by Dehn surgery on \(L\) admit complete hyperbolic structures. In this work some local problems proposed in an earlier paper are adressed and it is shown that for hyperbolic 3-manifolds \(M\) obtained from Thurston's construction, the structures in an open neighbourhood of the hyperbolic structure can be characterized by some similarity structures on the links of the components of \(L\) satisfying certain conditions. This is done without using extra parameters.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 938532
zbMATH Keywords: quasi-Fuchsian structures
zbMATH Keywords: hyperbolic 3-manifolds
author: Ser Peow Tan
reviewed by: Ismail Naci Cangül
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 938532