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

 

Geodesic ideal triangulations exist virtually


Authors: Feng Luo, Saul Schleimer and Stephan Tillmann
Journal: Proc. Amer. Math. Soc. 136 (2008), 2625-2630
MSC (2000): Primary 57N10, 57N15; Secondary 20H10, 22E40, 51M10
Published electronically: March 10, 2008
MathSciNet review: 2390535
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Abstract: It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, 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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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/S0002-9939-08-09387-8
PII: S 0002-9939(08)09387-8
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 (DMS-0508971).
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