Line arrangements in $\mathbb {H}^3$
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- by Peter Milley PDF
- Proc. Amer. Math. Soc. 133 (2005), 3115-3120 Request permission
Abstract:
If $M=\mathbb {H}^3/G$ is a hyperbolic manifold and $\gamma \subset M$ is a simple closed geodesic, then $\gamma$ lifts to a collection of lines in $\mathbb {H}^3$ acted upon by $G$. In this paper we show that such a collection of lines cannot contain a particular type of subset (called a bad triple) unless $G$ has orientation-reversing elements. This fact allows us to extend certain lower bounds on hyperbolic volume to the non-orientable case.References
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Additional Information
- Peter Milley
- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544-1000
- Address at time of publication: Department of Mathematics, University of California–Riverside, Riverside, California 92521-0135
- Email: milley@math.princeton.edu, milley@math.ucr.edu
- Received by editor(s): April 15, 2004
- Received by editor(s) in revised form: June 3, 2004
- Published electronically: April 20, 2005
- Additional Notes: The author was supported in part by NSF Grants DMS-9505253 and DMS-0071852.
The author would like to thank David Gabai for his comments and support, and the reviewer for his comments and corrections. - Communicated by: Ronald A. Fintushel
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3115-3120
- MSC (2000): Primary 57M60, 51M09; Secondary 57M50
- DOI: https://doi.org/10.1090/S0002-9939-05-07875-5
- MathSciNet review: 2159793
Dedicated: Dedicated to my wife, Cheryl