Construction and Recognition of Hyperbolic 3-Manifolds with Geodesic Boundary

@inproceedings{Frigerio2008ConstructionAR,
  title={Construction and Recognition of Hyperbolic 3-Manifolds with Geodesic Boundary},
  author={Frigerio and Petronio},
  year={2008}
}
We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston’s approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and we discuss consistency and completeness equations. Moreover, building on previous work of Ushijima, we extend Weeks’ tilt formula algorithm, which computes the Epstein-Penner canonical triangulation, to an algorithm that computes the Kojima triangulation. The… CONTINUE READING
10 Citations
15 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 15 references

Convex hulls and isometries of cusped hyperbolic 3-manifolds

  • J. R. Weeks
  • Topology Appl
  • 1993
Highly Influential
6 Excerpts

Polyhedral decomposition of hyperbolic manifolds with boundary

  • S. Kojima
  • Proc. Work. Pure Math
  • 1990
Highly Influential
10 Excerpts

A unified viewpoint about geometric objects in hyperbolic space and the generalized tilt formula, In: “Hyperbolic spaces and related topics, II, Kyoto, 1999

  • A. Ushijima
  • Sūrikaisekikenkyūsho Kōkyūroku
  • 2000
Highly Influential
4 Excerpts

The geometry of discrete groups

  • A. F. Beardon
  • Graduate Texts in Mathematics,
  • 1995

Lectures in Hyperbolic Geometry

  • R. Benedetti, C. Petronio
  • Universitext, Springer-Verlag, Berlin,
  • 1992
2 Excerpts

Polyhedral decomposition of hyperbolic 3-manifolds with totally geodesic boundary, In: “Aspects of low-dimensional manifolds, Kinokuniya, Tokyo

  • S. Kojima
  • Adv. Stud. Pure Math
  • 1992
2 Excerpts

Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology

  • V. G. Turaev, O.Ya
  • 1992
1 Excerpt

Hyperbolic 3-manifolds with totally geodesic boundary

  • M. Fujii
  • Osaka J. Math
  • 1990
1 Excerpt

Similar Papers

Loading similar papers…