Construction of Acylindrical Hyperbolic 3-Manifolds with Quasifuchsian Boundary

Abstract

We construct a one (real) dimensional deformation of an acylindrical hyperbolic 3-manifold, compute some associated arithmetic invariants and exhibit the skinning map along the deformation locus. The key idea is to construct a one-dimensional family of hyperbolic polyhedra; reflections in some of the faces of the polyhedra then generate a family of Kleinian groups.

Keywords:

• Hyperbolic geometry
• Hyperbolic polyhedron
• Skinning map

Declaration of Interest

No potential conflict of interest was reported by the author(s).

Notes

1 See www.geomview.org.