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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An inequality for polyhedra
and ideal triangulations
of cusped hyperbolic 3-manifolds


Authors: Masaaki Wada, Yasushi Yamashita and Han Yoshida
Journal: Proc. Amer. Math. Soc. 124 (1996), 3905-3911
MSC (1991): Primary 57Q15, 52B05; Secondary 57M50, 51M20
MathSciNet review: 1346992
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Abstract | References | Similar Articles | Additional Information

Abstract: It is not known whether every noncompact hyperbolic 3-manifold of finite volume admits a decomposition into ideal tetrahedra. We give a partial solution to this problem: Let $M$ be a hyperbolic 3-manifold obtained by identifying the faces of $n$ convex ideal polyhedra $P_{1},\dots ,P_{n}$. If the faces of $P_{1},\dots ,P_{n-1}$ are glued to $P_{n}$, then $M$ can be decomposed into ideal tetrahedra by subdividing the $P_{i}$'s.


References [Enhancements On Off] (What's this?)

  • 1. D. B. A. Epstein and R. C. Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988), no. 1, 67–80. MR 918457 (89a:57020)
  • 2. Martin Hildebrand and Jeffrey Weeks, A computer generated census of cusped hyperbolic 3-manifolds, Computers and mathematics (Cambridge, MA, 1989) Springer, New York, 1989, pp. 53–59. MR 1005959 (90f:57043)
  • 3. W. Thurston, The Geometry and Topology of Three-Manifolds, Lecture Notes, Princeton University, 1978.
  • 4. H. Yoshida, Ideal tetrahedral decompositions of hyperbolic 3-manifolds, Osaka J. Math. 33 (1996), 37-46. CMP 96:10

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Additional Information

Masaaki Wada
Affiliation: Faculty of Science, Nara Women’s University, Kita-Uoya Nishimachi, Nara 630, Japan
Email: wada@ics.nara-wu.ac.jp

Yasushi Yamashita
Affiliation: Faculty of Science, Nara Women’s University, Kita-Uoya Nishimachi, Nara 630, Japan
Email: yamasita@ics.nara-wu.ac.jp

Han Yoshida
Affiliation: Faculty of Science, Nara Women’s University, Kita-Uoya Nishimachi, Nara 630, Japan
Email: han@ics.nara-wu.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03563-0
PII: S 0002-9939(96)03563-0
Keywords: Hyperbolic 3-manifold, triangulation
Received by editor(s): June 15, 1995
Communicated by: Ronald Stern
Article copyright: © Copyright 1996 American Mathematical Society