The Margulis invariant for parabolic transformations
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- by Virginie Charette and Todd A. Drumm PDF
- Proc. Amer. Math. Soc. 133 (2005), 2439-2447 Request permission
Abstract:
In this note, we extend the definition of Margulis’ signed Lorentz- ian displacement to parabolic transformations in $SO(2,1)\ltimes \mathbb {R}^{2,1}$. We show that the standard propositions about the “sign” of the transformations all hold true for parabolic elements also. In particular, we show that Margulis’ opposite sign lemma holds.References
- Todd A. Drumm, Fundamental polyhedra for Margulis space-times, Topology 31 (1992), no. 4, 677–683. MR 1191372, DOI 10.1016/0040-9383(92)90001-X
- Todd A. Drumm, Examples of nonproper affine actions, Michigan Math. J. 39 (1992), no. 3, 435–442. MR 1182499, DOI 10.1307/mmj/1029004598
- Todd A. Drumm and William M. Goldman, The geometry of crooked planes, Topology 38 (1999), no. 2, 323–351. MR 1660333, DOI 10.1016/S0040-9383(98)00016-0
- David Fried and William M. Goldman, Three-dimensional affine crystallographic groups, Adv. in Math. 47 (1983), no. 1, 1–49. MR 689763, DOI 10.1016/0001-8708(83)90053-1
- G. A. Margulis, Free completely discontinuous groups of affine transformations, Dokl. Akad. Nauk SSSR 272 (1983), no. 4, 785–788 (Russian). MR 722330
- G. A. Margulis, Complete affine locally flat manifolds with a free fundamental group, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 134 (1984), 190–205 (Russian, with English summary). Automorphic functions and number theory, II. MR 741860
- Mess, G., Lorentz spacetimes of constant curvature, preprint.
- John Milnor, On fundamental groups of complete affinely flat manifolds, Advances in Math. 25 (1977), no. 2, 178–187. MR 454886, DOI 10.1016/0001-8708(77)90004-4
Additional Information
- Virginie Charette
- Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4L7
- Email: charette@math.mcmaster.ca
- Todd A. Drumm
- Affiliation: Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081
- Address at time of publication: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
- Email: tad@swarthmore.edu, tad@math.upenn.edu
- Received by editor(s): February 14, 2003
- Published electronically: March 21, 2005
- Communicated by: Wolfgang Ziller
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 2439-2447
- MSC (2000): Primary 53A15; Secondary 83A05
- DOI: https://doi.org/10.1090/S0002-9939-05-08137-2
- MathSciNet review: 2138887