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Crooked planes
Author(s):
Todd
A.
Drumm;
William
M.
Goldman
Journal:
Electron. Res. Announc. Amer. Math. Soc.
1
(1995),
10-17.
MSC (1991):
Primary 51
MathSciNet review:
1336695
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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.
References:
- 1
- Auslander,L. and Markus, L., Holonomy of flat affinely connected manifolds, American J. Math. 62 (1955), 139--159 MR 17:298b
- 2
- ------ Flat Lorentz 3-manifolds, Memoirs Amer. Math. Soc. 30 (1959) MR 24:A1689
- 3
- Drumm, T., Fundamental polyhedra for Margulis space-times, Topology 31 (4) (1992), 677-683 MR 94a:57051
- 4
- ------, Linear holonomy of Margulis space-times, J.Diff.Geo. 38 (1993), 679--691 MR 94a:57051
- 5
- ------, Examples of nonproper affine actions, Mich. Math. J. 39 (1992), 435--442 MR 93j:57022
- 6
- ------, Margulis space-times, Proc. Symp. Pure Math. 54 (1993), Part 2, 191--195 MR 94a:00011
- 7
- ------, Translations and the holonomy of complete affine flat manifolds (preprint) CMP 95:05
- 8
- Drumm, T. and Goldman, W., Complete flat Lorentz 3-manifolds with free fundamental group, Int. J. Math.1 (1990), 149--161 MR 91f:57022
- 9
- ------, The geometry of crooked planes, preprint, 30 pp.
- 10
- Fried, D. and Goldman, W., Three-dimensional affine crystallographic groups, Adv. Math. 47 (1983), 1--49 MR 84d:20047
- 11
- Goldman, W., ``Complex hyperbolic geometry,'' Oxford Mathematical Monographs (to appear)
- 12
- Margulis, G., Free properly discontinuous groups of affine transformations, Dokl. Akad. Nauk SSSR 272 (1983), 937--940; MR85e:22015
- 13
- ------, Complete affine locally flat manifolds with a free fundamental group, J. Soviet Math. 134 (1987), 129--134 MR 86h:22019
- 14
- Mess, G., Lorentz spacetimes of constant curvature, (preprint)
- 15
- Milnor, J., On fundamental groups of complete affinely flat manifolds, Adv. Math. 25 (1977), 178--187
- 16
- Tits, J., Free subgroups in linear groups, J. Algebra 20 (1972), 250--270 MR 44#4105
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Additional Information:
Todd
A.
Drumm
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104
Email:
tad@math.upenn.edu
William
M.
Goldman
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742
Email:
wmg@math.umd.edu
DOI:
10.1090/S1079-6762-95-01002-X
PII:
S 1079-6762(95)01002-X
Keywords:
Space-times,
affine,
fundamental polyhedra,
crooked planes
Received by editor(s):
March 11, 1995
Additional Notes:
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.
Communicated by:
Gregory Margulis
Copyright of article:
Copyright
1995,
American Mathematical Society
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