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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. |
Keywords
hyperbolic manifold, canonical triangulation, Dehn fillings
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Mathematical Subject Classification 2010
Primary: 51H20
Secondary: 57M50
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References |
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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Authors |
| François Guéritaud | |
| Laboratoire Paul–Painlevé CNRS UMR 8524 Université de Lille 1 59650 Villeneuve d’Ascq France |
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| Saul Schleimer | |
| Mathematics Institute University of Warwick Coventry CV4 7AL UK |
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| http://www.warwick.ac.uk/~masgar/ | |
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