Volume 14, issue 1 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Canonical triangulations of Dehn fillings

François Guéritaud and Saul Schleimer

Geometry & Topology 14 (2010) 193–242
Abstract

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