Mathematische Annalen

, Volume 322, Issue 3, pp 563–571

The uniqueness of polynomial crystallographic actions

  • Yves Benoist
  • Karel Dekimpe
Original article

DOI: 10.1007/s002080200005

Cite this article as:
Benoist, Y. & Dekimpe, K. Math Ann (2002) 322: 563. doi:10.1007/s002080200005


Let \(\Gamma\) be a polycyclic-by-finite group. It is proved in [8] that \(\Gamma\) admits a polynomial action of bounded degree on \(\mathbb{R}^n\) which is properly discontinuous and such that the quotient \(\Gamma\backslash \mathbb{R}^n\) is compact. We prove here that such an action is unique up to conjugation by a polynomial transformation of \(\mathbb{R}^n\).

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Yves Benoist
    • 1
  • Karel Dekimpe
    • 2
  1. 1.Ecole Normale Supérieure, 45 rue d'Ulm 75230 Paris, France (e-mail: FR
  2. 2.Katholieke Universiteit Leuven, Campus Kortrijk, B–8500 Kortrijk, Belgium (e-mail: BE