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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Margulis invariant for parabolic transformations


Authors: Virginie Charette and Todd A. Drumm
Journal: Proc. Amer. Math. Soc. 133 (2005), 2439-2447
MSC (2000): Primary 53A15; Secondary 83A05
Published electronically: March 21, 2005
MathSciNet review: 2138887
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Abstract: In this note, we extend the definition of Margulis' signed Lorentzian 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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08137-2
PII: S 0002-9939(05)08137-2
Received by editor(s): February 14, 2003
Published electronically: March 21, 2005
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2005 American Mathematical Society