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Crooked planes are polyhedra used to construct fundamental polyhedra for discrete groups of Lorentz isometries acting properly on Minkowski (2+1)-space. These fundamental polyhedra are regions bounded by disjoint crooked planes. We develop criteria for the intersection of crooked planes and apply these criteria to proper discontinuity of discrete isometry groups.

Copyright American Mathematical Society 1995

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Article Info

• ERA Amer. Math. Soc. 01 (1995), pp. 10-17
• Publisher Identifier: S 1079-6762(95)01002-7
• 1991 Mathematics Subject Classification. 51.
• Key words and phrases. Space-times, affine, fundamental polyhedra, crooked planes
• Received by the editors March 11, 1995
• Communicated by Gregory Margulis
• Comments (When Available)

Todd A. Drumm

Department of Mathematics
University of Pennsylvania
Philadelphia, PA 19104

E-mail address: tad@math.upenn.edu

William M. Goldman

Department of Mathematics
University of Maryland
College Park, MD 20742

E-mail address: wmg@math.umd.edu

Goldman was partially supported by NSF grant DMS-8902619 and the University of Maryland Institute for Advanced Computer Studies. Drumm was partially supported by an NSF Postdoctoral fellowship, and thanks Swarthmore College's KIVA project for their hospitality.