Line arrangements in
Proc. Amer. Math. Soc. 133 (2005), 3115-3120
Primary 57M60, 51M09; Secondary 57M50
April 20, 2005
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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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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
Received by editor(s):
April 15, 2004
Received by editor(s) in revised form:
June 3, 2004
April 20, 2005
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 to my wife, Cheryl
Ronald A. Fintushel
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American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.