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Crooked Planes
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## Crooked planes

### Todd A. Drumm and William M. Goldman

**Abstract.**
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.

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