Geodesic ideal triangulations exist virtually
Authors:
Feng Luo, Saul Schleimer and Stephan Tillmann
Journal:
Proc. Amer. Math. Soc. 136 (2008), 26252630
MSC (2000):
Primary 57N10, 57N15; Secondary 20H10, 22E40, 51M10
Published electronically:
March 10, 2008
MathSciNet review:
2390535
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: It is shown that every noncompact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with nonempty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.
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 YoungEun Choi: Positively oriented ideal triangulations on hyperbolic threemanifolds, Topology 43, no. 6, 13451371 (2004). MR 2081429 (2005i:57016)
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 David B. A. Epstein and Robert C. Penner: Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27, no. 1, 6780 (1988). MR 918457 (89a:57020)
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 Roberto Frigerio: On deformations of hyperbolic manifolds with geodesic boundary, Algebr. Geom. Topol. 6, 435457 (2006). MR 2220684 (2007b:57027)
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 John Hudson: Piecewise linear topology, University of Chicago Lecture Notes, W. A. Benjamin, Inc., New YorkAmsterdam, 1969. MR 0248844 (40:2094)
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 Sadayoshi Kojima: Polyhedral decomposition of hyperbolic manifolds with totally geodesic boundary. Aspects of lowdimensional manifolds, 93112, Adv. Stud. Pure Math., 20, Kinokuniya, Tokyo, 1992. MR 1208308 (94c:57023)
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 Sadayoshi Kojima: Polyhedral Decomposition of Hyperbolic Manifolds with Boundary, On the geometric structure of manifolds, edited by Dong Pyo Chi, Proc. of Workshop in Pure Math., 10, part III, 3757 (1990).
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 Darren D. Long and Graham A. Niblo: Subgroup separability and manifold groups, Math. Z. 207, no. 2, 209215 (1991). MR 1109662 (92g:20047)
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 Walter D. Neumann and Don Zagier: Volumes of hyperbolic threemanifolds, Topology 24, 307332 (1985). MR 815482 (87j:57008)
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 Carlo Petronio and Joan Porti: Negatively oriented ideal triangulations and a proof of Thurston's hyperbolic Dehn filling theorem, Expo. Math. 18, no. 1, 135 (2000). MR 1751141 (2001c:57017)
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 John G. Ratcliffe: Foundations of hyperbolic manifolds, Graduate Texts in Mathematics, 149, SpringerVerlag, New York, 1994. MR 1299730 (95j:57011)
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 William P. Thurston: The geometry and topology of manifolds, Princeton Univ. Math. Dept. (1978). Available from http://msri.org/publications/books/gt3m/.
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Additional Information
Feng Luo
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
Email:
fluo@math.rutgers.edu
Saul Schleimer
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08854
Email:
saulsch@math.rutgers.edu
Stephan Tillmann
Affiliation:
Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia
Email:
tillmann@ms.unimelb.edu.au
DOI:
http://dx.doi.org/10.1090/S0002993908093878
PII:
S 00029939(08)093878
Keywords:
Hyperbolic manifold,
ideal triangulation,
partially truncated triangulation,
subgroup separability
Received by editor(s):
April 9, 2007
Published electronically:
March 10, 2008
Additional Notes:
The research of the first author was supported in part by the NSF
The second author was partly supported by the NSF (DMS0508971).
The third author was supported under the Australian Research Council’s Discovery funding scheme (project number DP0664276).
This work is in the public domain.
Communicated by:
Daniel Ruberman
