Line arrangements in
Author: Peter Milley
Journal: Proc. Amer. Math. Soc. 133 (2005), 3115-3120
MSC (2000): Primary 57M60, 51M09; Secondary 57M50
Published electronically: April 20, 2005
MathSciNet review: 2159793
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Abstract: If is a hyperbolic manifold and is a simple closed geodesic, then lifts to a collection of lines in acted upon by . In this paper we show that such a collection of lines cannot contain a particular type of subset (called a bad triple) unless has orientation-reversing elements. This fact allows us to extend certain lower bounds on hyperbolic volume to the non-orientable case.
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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: firstname.lastname@example.org, email@example.com
Keywords: Hyperbolic geometry, non-orientable manifolds
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.
Dedicated: Dedicated to my wife, Cheryl
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.