Canonical triangulations of Dehn fillings

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. As an example, we treat all hyperbolic fillings on one cusp of the Whitehead link complement.

37 pages, 12 figures

References in corpus (3)

• Layered-triangulations of 3-manifolds
• Angled decompositions of arborescent link complements
• Triangulated cores of punctured-torus groups

Cited by in corpus (8)

• 1-efficient triangulations and the index of a cusped hyperbolic 3-manifold
• On minimal ideal triangulations of cusped hyperbolic 3-manifolds
• Dehn filling and the geometry of unknotting tunnels
• Geometric triangulations and highly twisted links
• Hyperbolic Knot Theory
• Geometric triangulations of a family of hyperbolic 3-braids
• Infinitely many virtual geometric triangulations
• A-polynomials, Ptolemy equations and Dehn filling