Geometry & Topology 14 (2010) 193–242

DOI: 10.2140/gt.2010.14.193

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

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