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Canonical triangulations of Dehn fillings
François Guéritaud and Saul Schleimer
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Geometry & Topology 14 (2010)
193–242
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Abstract
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Every cusped, finite-volume hyperbolic three-manifold has a canonical decomposition
into ideal polyhedra. We study the canonical decomposition of the hyperbolic
manifold obtained by filling some (but not all) of the cusps with solid tori: in a broad
range of cases, generic in an appropriate sense, this decomposition can be predicted
from that of the unfilled manifold (a similar result has been independently announced
by Akiyoshi [Kokyuroku 1329, RIMS, Kyoto (2003) 121-132]). We also find the
canonical decompositions of all hyperbolic Dehn fillings on one cusp of the
Whitehead link complement.
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Keywords
hyperbolic manifold, canonical
triangulation, Dehn fillings
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Mathematical Subject Classification
Primary: 51H20
Secondary: 57M50
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Publication
Received: 29 July 2008
Revised: 22 September 2009
Accepted: 26 August 2009
Preview posted: 21 October 2009
Published: 2 January 2010
Proposed: David Gabai
Seconded: Walter Neumann, Joan Birman
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