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

DOI:
https://doi.org/10.1090/S0002-9939-08-09387-8

Published electronically:
March 10, 2008

MathSciNet review:
2390535

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-08-09387-8

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